The Physics of Sound

Introduction

There is a particular kind of stuck that happens to technicians who have learned the controls but not the reasons. They can set a gain, patch a system and ring out a room, and they are genuinely useful. But when something behaves oddly — a microphone that sounds hollow, a speaker that is loud at the front and thin at the back, a bass note that vanishes if you take two steps left — they have no way to reason about it. They try things. Sometimes one works, and they never find out why.

The difference between guessing and diagnosing is a handful of physical facts. Not many, and none of them difficult. This book is those facts.

What this book actually does

It explains what sound is, how it travels, and what happens when it meets a room, a surface or another copy of itself. Every idea is connected to something you will actually do: why moving a microphone closer beats adding gain, why a room needs delay speakers, why two mics on one source can sound worse than one.

It is deliberately not a physics textbook. There is no calculus and very little algebra — one equation, used constantly. What there is instead is numbers you can carry: the length of a wave at a given frequency, how much level you lose over a distance, how far apart two microphones need to be.

Who this is for

• Technicians who can operate the equipment but have never been told why it behaves as it does.
• Anyone moving from general crew into audio, where the reasoning matters more than the button.
• People who learned by watching, and now find the gaps showing under pressure.
• Working engineers who want the underlying facts stated plainly once, in the language a crew actually uses.
• Experienced professionals who need to explain this to the people they bring on, and want an ordered way to do it.

What this book will not do

It will not make you an acoustician or a system designer. Those are specialisms with their own mathematics and their own software. What it will do is let you look at a problem on a show floor and reason about it from first principles instead of trying settings until something changes.

How to Use This Book

Each chapter follows the same shape as every other book in this track. You read the idea, then the numbers behind it, then the same material as a real situation, then a procedure, then what goes wrong, then you practice.

1. Read the chapter body first. It is written to be read straight through.
2. Read The numbers. This is where the figures live, and the figures are the point of a physics book.
3. Read On the job, where the idea appears on a real show.
4. Work through How to do it. These are things you can do on a job this week.
5. Study What goes wrong. Most of these will be familiar; the value is in the cause column.
6. Do the exercise before reading the answer. Recognition feels like learning and is not.

Keep a notebook

One habit is worth starting before the first chapter, and it matters more in this book than in most: keep a small notebook and write the numbers in it as you meet them. This is a book of quantities. The speed of sound, the wavelength of 100 Hz, what six decibels does to a distance, where critical distance sits in a live room, how long a reverberant tail runs before it stops being useful. You will want every one of them on a job and you will remember almost none of them from one reading.

Write them by hand rather than photographing the page. Copying a number puts it on paper; rewriting it in your own words is what puts it in your head, and working out how to phrase it is most of the learning. Add the ones you meet at work too — the room that sounded wrong and why, the distance where the delay finally landed, the frequency that always feeds back in that venue.

Then read a few pages of it on the way to a job. Five minutes turns things you half-know into things you know, and the moment you need to know whether a wavelength is longer than the gap you are trying to put it through is never a moment when you can stop and look it up.

A note on numbers

Every figure in this book is rounded to something you can hold in your head. The speed of sound is 343 metres per second, not 343.2. A thousand-hertz wave is 34 centimetres, not 34.3. Precision beyond that is false comfort: the temperature in the room moves the answer more than the rounding does.

A note on safety

This book discusses sound pressure levels that cause permanent hearing damage. Hearing loss is cumulative, painless while it happens, and does not come back. Know the exposure limits where you work, carry protection, and use it.

Where this book sits

This book assumes no audio experience and no mathematics beyond doubling and halving. It is a first book and it stands on its own.

What pairs with this

• Audio Basics — the what to this book's why — they overlap on purpose

Where it leads

These are not steps in an order. Take whichever one fits.

• Audio Basics — the equipment that puts these ideas to work
• Front-of-House Mixing — if you already know the gear and want to mix

What Sound Actually Is

Everything else in audio is a consequence of one fact: sound is a pressure wave moving through air.

Pressure, not stuff

Sound is a change in air pressure that travels. A loudspeaker cone pushes forward and squeezes the air just in front of it, making a region of slightly higher pressure. It pulls back and leaves a region of slightly lower pressure. That pattern of squeeze and release moves outward through the room at about 343 metres per second, and when it reaches an eardrum or a microphone diaphragm it pushes and pulls that too. What you hear is your eardrum copying the movement of the speaker cone, a fraction of a second later.

The single most useful thing to understand is that the air itself does not travel. Individual air molecules jostle their neighbours and return to roughly where they started. The pattern travels; the material does not. This is why a wind machine is not a loudspeaker and why blowing at a microphone is not the same as speaking into it. It is also why sound needs a medium at all: in a vacuum there is nothing to squeeze, so there is no sound, however much energy you put in.

The pressure changes involved are astonishingly small. Normal atmospheric pressure is about 101,325 pascals. The quietest sound a healthy young person can hear is a pressure variation of about 0.00002 pascals — roughly one five-billionth of the pressure already pressing on your eardrum. A painfully loud rock concert is around 20 pascals, still only two ten-thousandths of atmospheric pressure. Hearing is a fantastically sensitive differential measurement, not a strong one.

Why it matters on a show floor

Everything a technician does to sound is a manipulation of that travelling pressure pattern. A microphone converts it into a voltage that varies the same way. A cable carries that voltage. A console adds, subtracts and reshapes it. An amplifier makes it large enough to move a cone, and a loudspeaker turns it back into moving air. At every stage the shape of the wave is the thing being preserved or damaged, and every fault you will ever chase is a place where the shape changed when it should not have.

It also explains why rooms matter so much. A pressure wave does not stop at the audience. It carries on to the back wall, bounces, and comes back through the audience a second time, later and quieter. The room is not a container that sound sits inside; it is part of the signal path, and an uncontrolled one. A system that measures perfectly in a warehouse can sound wrong in a ballroom for reasons that have nothing to do with the equipment.

Sound needs something to carry it, and something to catch it

A wave of pressure has to be a wave of pressure in something. Air is the usual something, but sound travels through water, steel, concrete and a wooden stage floor, and it travels faster through each of them than through air because their molecules are packed closer and pass the push along sooner. It does not travel through a vacuum at all. There is nothing to squeeze.

That is not a curiosity. It is why a subwoofer on a hollow stage deck is heard by the room and felt through the feet of everyone standing on it, arriving by two routes at two speeds. It is why an isolated wall works by breaking the physical path rather than by absorbing anything. And it is why the phrase "sound-proofing" usually means the wrong thing: a soft panel on a wall changes the reflections inside the room and does very little about what gets through the wall, which travels as vibration in the structure rather than as a wave in the air.

The other end of the chain matters just as much. Something has to catch the wave and turn it into a signal. That is transduction, and it is the same trick in both directions: a microphone lets the pressure wave move a diaphragm, and turns that motion into a voltage; a loudspeaker takes a voltage, moves a cone, and pushes air. A microphone is a loudspeaker running backwards, and the reason a large loudspeaker cannot reproduce high frequencies is the same reason a large diaphragm microphone hears them differently — mass takes time to move.

Everything in the rest of this book happens between those two transducers, and everything in the rest of your career happens between them too. The pressure wave is real; the voltage is a copy of it; and every problem you will ever chase is either a fault in the copying or a fault in the room.

The numbers behind a pressure wave

Sound is a change in pressure, and the changes are far smaller than most people expect. These are the figures that make the scale of the thing concrete.

What travels, and what does not

• The pattern of pressure travels. The air does not. Molecules jostle their neighbours and return to roughly where they started.
• This is why a fan is not a loudspeaker, and why wind noise on a microphone is a different mechanism from sound.
• A vacuum carries no sound at any level, because there is nothing to compress.
• Denser media carry sound faster, not louder. Steel carries it at about 5,000 m/s, which is why you hear a train through a rail before you hear it through the air.

On the job

You are standing in an empty ballroom at eight in the morning with a single loudspeaker on a stick and a laptop playing pink noise. It sounds fine where you are, three metres away. You walk to the back wall, twenty metres out, and it sounds distant and dull, which you expected. Then you walk back along the side of the room and, about two-thirds of the way forward, the low end almost disappears for a couple of paces before coming back.

Nothing has changed about the speaker, the laptop or the cable. What changed is where you are standing in a pattern of pressure that fills the whole room. The direct sound from the speaker is arriving at your ears, and so is the same sound a fraction later after bouncing off the back wall. In most places those two add up to something reasonable. In a few places, for a particular range of frequencies, they arrive opposed and subtract instead.

An hour later the room is full of people and chairs and the effect is much weaker, because most of that reflected energy is now being absorbed by clothing and bodies before it can come back. This is the whole subject in one morning: the equipment was never the variable.

How to do it

1. Stand at the mix position and listen to a familiar track, so you have a reference for the room rather than for the system.
2. Walk the room slowly along one axis, listening for places where the low end thickens or thins. Note where they are.
3. Walk the other axis and do the same. The pattern is usually symmetrical about the room's centre lines.
4. Look at what the room is made of. Hard, sealed, parallel surfaces make strong reflections; soft, broken, angled ones make weak ones.
5. Check whether the audience will be standing where the worst of it is, because that is the only place it matters.
6. Repeat once the room is dressed and populated, because both change the answer substantially.

What goes wrong

Practice it

Answer from the physics, before checking.

Frequency, Wavelength and Pitch

One equation connects the note you hear, the size of the wave in the room, and half the decisions you will make about gear.

Cycles per second

If the speaker cone moves in and out 100 times a second, the pressure wave has 100 complete cycles per second. That is its frequency, measured in hertz, and it is what you perceive as pitch. Low frequencies are slow oscillations; high frequencies are fast ones. Human hearing runs from roughly 20 Hz to 20,000 Hz, though the top of that range falls with age and exposure, and most adults working in this industry have lost some of it.

Musical pitch maps onto frequency logarithmically, not linearly. Doubling the frequency raises the pitch by one octave, whatever the starting point. 110 Hz to 220 Hz is an octave; 5,000 Hz to 10,000 Hz is also an octave. This is why frequency controls on a console are spaced logarithmically, why a graphic equaliser's bands get wider apart as they go up, and why the range from 20 Hz to 200 Hz — only 180 Hz wide — contains as much musical territory as 2,000 Hz to 20,000 Hz.

Wavelength is a physical size

Because the wave travels at a fixed speed, its frequency determines its physical length. The relationship is wavelength equals speed divided by frequency. At 343 metres per second, a 20 Hz wave is about 17 metres long, a 100 Hz wave about 3.4 metres, a 1,000 Hz wave about 34 centimetres, and a 10,000 Hz wave about 3.4 centimetres. These are not abstractions; they are measurements you could take with a tape.

Once you can picture the size of a wave, a great deal of behaviour stops being mysterious. A wave much larger than an object flows around it as if it were not there, which is why a bass guitar is audible through a wall and a hi-hat is not, and why standing in front of a subwoofer does not block it. A wave much smaller than an object reflects off it like light off a mirror, which is why high frequencies are so directional and why a person standing between a speaker and a microphone changes the sound. Every acoustic effect you will meet is really a question about the size of the wave relative to the size of the thing it met.

Turning a wave into numbers — sampling and bit depth

Everything so far has been about a continuous pressure wave in air. Every console you will ever sit at turns that wave into numbers first, and two of those numbers are printed on the front of the box. They are worth understanding, because both of them are consequences of the physics in this chapter rather than facts about computers.

SAMPLING is measuring the wave's level at regular intervals and writing down the result. The sample rate is how many times a second that happens: 48,000 in professional audio, written 48 kHz, and 44.1 kHz on a compact disc.

Why 48,000 and not 20,000, when hearing stops around 20 kHz? Because of one rule, and it is a frequency rule. To capture a wave you need at least two samples per cycle — one for the crest and one for the trough. Fewer than that and you cannot tell the wave apart from a slower one. So the highest frequency a system can represent is half the sample rate, and that half is called the Nyquist frequency. At 48 kHz the ceiling is 24 kHz, comfortably above hearing, and the headroom above 20 kHz is what the filters need in order to be gentle.

What happens if a frequency above the Nyquist limit arrives anyway is worth knowing, because it is not the harmless silence you would expect. It does not disappear and it does not simply cut off. It folds back down and reappears as a lower frequency that was never there — a 30 kHz tone into a 48 kHz system comes back as an audible 18 kHz whistle that no EQ can remove, because at that point it is genuinely part of the signal. This is aliasing, and it is why every converter has a filter in front of it whose only job is to remove what the system cannot represent, before it gets the chance to fold.

BIT DEPTH is how precisely each of those measurements is written down. Sixteen bits gives about 65,000 possible levels, twenty-four bits gives about sixteen million. Bit depth has nothing to do with frequency and everything to do with the distance between the loudest thing the system can hold and the quietest thing it can distinguish from nothing — the dynamic range. Roughly six decibels per bit: 16-bit gets you about 96 dB, 24-bit about 144 dB, which is more than any room or microphone will ever hand you.

That is the practical point of 24-bit, and it is not fidelity in any audible sense. It is headroom you are allowed to waste. With that much range you can set a gain conservatively, leave twenty decibels unused at the top so nothing ever clips, and still be nowhere near the noise floor. On 16-bit that same caution costs you real quality, which is why old digital recordings were made close to the limit and modern ones are not.

And the one hard edge to remember: unlike analogue, digital does not distort gracefully. There is a maximum number, and a signal that exceeds it is not squashed, it is truncated flat, which is audible immediately and unrecoverable. Full scale is a wall rather than a slope. This is why the digital meter's top is called 0 dBFS — full scale, the number itself — and why the whole discipline of gain structure exists to keep you away from it.

Where real sources actually live

Knowing that frequency is cycles per second is arithmetic. Knowing where things sit is the part you use, because it tells you what a problem can and cannot be before you touch anything.

A speaking voice does most of its work between about 100 and 4,000 hertz. The fundamental — the note the voice is actually on — is roughly 85 to 180 hertz for a typical man and 165 to 255 for a typical woman, and it is a surprisingly small part of what makes speech understandable. Intelligibility lives higher, in the consonants, mostly between 2,000 and 4,000 hertz. This is why a muffled system is not fixed by adding bass, and why the difference between a presenter who can be followed and one who cannot is usually a couple of decibels in a band most people never think about.

A kick drum's body is around 60 to 100 hertz and its click is up at 3,000 to 5,000. A bass guitar's lowest string is about 41 hertz. A grand piano runs from 27 hertz to a little over 4,000, which is why it is the instrument most likely to expose a room's problems at both ends. Cymbals extend past 15,000. A cheap laptop speaker starts giving up below about 200, which is why a presenter's own laptop always sounds thinner than the system you have built.

Two things follow that are worth carrying. First, almost nothing musical has a fundamental below 40 hertz, so a system that struggles under 40 is missing very little except effects and the low end of a synth. Second, the range that matters most for the job you will be doing on most days — a person talking — is narrow, and it sits in the middle. A great deal of what people call "system tuning" is arranging for that narrow band to arrive intact.

Harmonics, and why two instruments on one note sound different

Almost nothing produces a single frequency. A tuning fork nearly does, which is why it sounds so plain. Everything else produces a fundamental plus a stack of harmonics above it — whole-number multiples of that fundamental, at various levels, changing as the note goes on.

A note at 100 hertz carries energy at 200, 300, 400 and upwards. The fundamental sets the pitch you hear. The pattern of harmonics above it is what makes a violin sound like a violin and a trumpet on the same note sound like a trumpet. That pattern is timbre, and it is the reason you can recognise a friend's voice in one syllable.

This has a practical consequence that surprises people. You can remove a note's fundamental entirely and most listeners will still hear the same pitch, because the harmonic series implies it — the ear reconstructs a fundamental that is no longer there. It is why a small loudspeaker with nothing under 150 hertz can still sound like it is playing a bass line, and why a phone can play music at all.

It also explains why a problem at one frequency rarely stays there. Distort a signal and you add harmonics that were not in the original; the ear hears them as harshness up in the consonant range even though the fault is somewhere else entirely.

Wavelength at frequencies you actually use

Wavelength equals the speed of sound divided by frequency. It is the only equation in this book, and knowing roughly what it gives at common frequencies explains more behaviour than anything else here.

What the size tells you

• A wave much larger than an object bends around it as if it were not there. Below about 100 Hz, most of a room's furniture is invisible to the sound.
• A wave much smaller than an object reflects off it. Above a few kilohertz, a person is a mirror, which is why a body between a speaker and a microphone changes the tone.
• Absorbers work on wavelengths comparable to their thickness. A 5 cm panel does useful work above 1 kHz and almost nothing at 100 Hz.
• Microphone spacing and speaker spacing both matter in wavelengths, not metres, which is why the same offset is harmless at 100 Hz and destructive at 5 kHz.

Octaves, and why the controls are spaced that way

• Doubling frequency raises pitch by one octave, wherever you start. 110 to 220 Hz and 5 to 10 kHz are both one octave.
• The audible range is about ten octaves. Half of them sit below 640 Hz.
• This is why 20–200 Hz holds as much musical territory as 2–20 kHz, and why console EQ frequency controls are logarithmic.

On the job

A presenter is on a lectern with a gooseneck microphone, and there is a loudspeaker on a stick about four metres to one side. The system rings at a frequency somewhere around 2.5 kHz as soon as you get the level up to where the back row needs it. The obvious answers have all been tried: the gain is as low as it can be, the EQ has a notch in it already, and the presenter will not move.

Think about the size. A 2.5 kHz wave is about 14 centimetres long. That is smaller than the presenter's head, smaller than the lectern's front panel, and much smaller than the loudspeaker's cabinet. At that wavelength the lectern is not an obstruction the sound flows around, it is a hard reflecting surface pointed at the microphone.

Turning the lectern five degrees, or moving the speaker forward half a metre so the microphone sits further off its axis, changes the geometry the wave is meeting. Both are free, take seconds, and are more effective than another filter, because the filter treats the symptom in the electrical domain while the cause is a reflection in the acoustic one.

How to do it

1. Work out the wavelength of the frequency causing trouble: 343 divided by the frequency in hertz gives metres.
2. Compare that length to the objects around the microphone and the loudspeaker.
3. If the wavelength is much smaller than the nearby objects, treat them as mirrors and change the angles.
4. If it is much larger, stop looking at nearby objects and look at the room's dimensions instead.
5. Change the geometry first — position, angle, distance — because it costs nothing and does not narrow the sound.
6. Only then reach for a filter, and use the narrowest one that does the job.

What goes wrong

Practice it

Calculate before you check. Speed of sound is 343 m/s.

Level, Loudness and the Decibel

The decibel is a ratio, not a quantity, and understanding that removes most of the confusion in audio.

Why the scale is logarithmic

Hearing spans an enormous range. The loudest sound you can tolerate involves a pressure variation about a million times larger than the quietest you can detect. Writing that range in ordinary units would mean numbers from 0.00002 to 20, which is unwieldy and misleading, because perception does not work in equal steps of pressure. It works in ratios: a sound has to be roughly ten times the intensity to be judged twice as loud.

The decibel matches the scale to the perception. It is a logarithmic ratio between two quantities, which means a decibel value on its own means nothing until you know what it is measured against. dB SPL is measured against the threshold of hearing. dBu and dBV are measured against fixed voltages. dBFS is measured against the maximum a digital system can represent, so it is always zero or negative. Confusing these is the single most common source of nonsense in audio conversation.

Some useful anchors: a 3 dB change is a doubling of power, and about the smallest change most people notice on programme material. A 6 dB change is a doubling of pressure. A 10 dB change is roughly a doubling of perceived loudness. And 0 dB does not mean silence — it means the two quantities being compared are equal.

Distance, and the inverse square law

Sound spreading freely from a small source loses 6 dB every time the distance doubles. Two metres from a source is 6 dB quieter than one metre; four metres is 12 dB quieter. This is the inverse square law, and it comes from geometry: the same energy is spread over a sphere whose area grows with the square of the radius.

It has direct consequences on a job. It explains why a vocalist who moves 15 centimetres away from a microphone drops significantly in level while one who moves 15 centimetres at the back of a room does not. It explains why moving a microphone closer is usually a better answer to a level problem than adding gain, because the wanted sound rises while the room's contribution does not. And it explains why a single loudspeaker cannot cover a deep room evenly: the front row and the back row cannot both be at a sensible level, which is the entire reason delay speakers exist.

Adding decibels, and why two loudspeakers are not twice as loud

Ask almost anyone on a crew what happens when you add a second identical loudspeaker and they will say it gets twice as loud. It does not, and the gap between what people expect and what actually happens causes a particular kind of argument on show days, so it is worth settling.

Two identical sources, playing the same thing, give you three decibels. Not double. Three. The reason is that decibels are a ratio and doubling the power is a ratio of two, which is what three decibels means. Doubling it again — four loudspeakers now — gives you another three, so four is six decibels above one. Eight is nine. You are paying exponentially for a scale that climbs by addition, which is the whole character of working with sound.

Three decibels is also, roughly, the smallest change most people notice on programme material. So the honest way to describe the second loudspeaker is that it is just perceptible, and that it doubles your cost. It is worth having for coverage, because it puts sound where the first one does not reach. It is a poor way to buy level.

A rule of thumb worth carrying: ten decibels is the doubling most people mean when they say twice as loud. That is ten times the power. If somebody wants a system that sounds twice as loud, they are asking for ten times the amplifiers, not two.

Two sources that are not identical add less tidily. If one is ten decibels below the other, the sum is essentially the louder one — the quieter contributes about half a decibel and vanishes into rounding. This is why one loud thing in a room dominates everything quieter than it, and why chasing a noise floor fifteen decibels down is chasing something the audience will never hear.

Which decibel, and what it is measured against

A decibel on its own means nothing. It is a ratio, and the suffix tells you what the comparison is. Most confusion in audio comes from treating these as interchangeable when they are not.

The changes worth memorising

• 3 dB is a doubling of power, and about the smallest change most people notice on music.
• 6 dB is a doubling of sound pressure, and the loss from doubling your distance from a source.
• 10 dB is roughly a doubling of perceived loudness, and takes ten times the power.
• 0 dB is not silence. It means the two quantities being compared are equal.

Distance and level

• Free-field sound loses 6 dB per doubling of distance. 1 m to 2 m loses 6 dB; 1 m to 4 m loses 12 dB.
• This is why a vocalist moving 15 cm off a close microphone changes level dramatically, and moving 15 cm at the back of a room changes nothing.
• It is also why one loudspeaker cannot serve a deep room: the front row and back row cannot both be right.
• Indoors the law holds only until the room's reflections dominate, after which level stops falling with distance and clarity falls instead.

On the job

A client asks for the room to be "twice as loud" during the awards section. The system is currently running at a comfortable 85 dB SPL at the mix position and there is plenty of headroom, so it sounds like an easy request.

Twice as loud means about 10 dB more, which means ten times the acoustic power. That is not a small ask. It takes the room to 95 dB SPL, which for an eight-hour day is at or beyond most exposure limits, and it will need close to ten times the amplifier power, which the rig may or may not have. Meanwhile a 3 dB increase — which doubles the power — will barely register as a change to the person asking.

The useful answer is not yes or no. It is to establish what they actually want, which is usually for the awards to feel bigger than the speeches. That is a contrast, and contrast is cheap: bring the speech sections down two or three decibels an hour earlier, and the awards will feel substantially louder without the system, the budget or anyone's hearing taking the strain.

How to do it

1. Establish the current level at the mix position with a meter, not a guess.
2. Ask what the request is really for — more impact, more intelligibility, or genuinely more level.
3. Convert any requested change into decibels and then into power, so the cost is visible.
4. Check the figure against the exposure limits that apply to the venue and the working day.
5. Look for contrast before reaching for level: lowering what came before is free.
6. If more level is genuinely needed, check headroom at the amplifier before promising it.

What goes wrong

Practice it

Answer before checking.

How Hearing Works

Everything so far has been about what sound does on its way across a room. This chapter is about the last six inches of that journey, because a system is only ever as good as what a person actually perceives, and hearing is not a flat measuring instrument. It is curved, adaptive and self-protecting, with strong opinions about frequency and about time.

Most of the mixing decisions that look like taste are that curve showing through. Learn its shape and a great deal of received wisdom stops being superstition and starts being arithmetic.

Hearing is not flat

A measurement microphone responds to 40 Hz and 4 kHz the same way. Your ear does not. Human hearing is most sensitive somewhere between 2 and 5 kHz — roughly the range of a baby's cry and a consonant — and falls away at both ends, steeply at the bottom.

The size of that fall is not fixed. It depends on how loud the sound is. At high levels the curve flattens out and you hear something close to the whole spectrum evenly. At low levels the ends collapse: bass disappears far faster than the midrange does, and the top loses some too. The classic measurements of this are the equal-loudness contours, and everyone in audio has met their consequence without necessarily knowing the name.

That consequence is this. A mix that sounds full and balanced at show level will sound thin and midrange-heavy at background level, and a mix balanced quietly will sound bass-heavy and shouty when you bring it up. Neither mix changed. Your ear did.

It is also why turning a system up makes it sound better, and why that is a trap. Level flatters. More of the spectrum arrives above your threshold, so more detail is audible, so it sounds like an improvement in quality when it is only an increase in quantity. Engineers who mix loud and then hand over a quiet system have made a system nobody else will like.

The working rule follows directly: judge tonal balance at the level the audience will hear, not at the level that is comfortable for you at the desk during setup. If the show runs at conversational level, set the tone at conversational level. Checking a mix at two very different levels takes thirty seconds and catches the problem before an audience does.

Masking, and why space beats level

Hearing does not evaluate each frequency independently. A loud sound raises the threshold for quieter sounds near it in frequency, so a quiet sound that would be perfectly audible on its own becomes inaudible in company. This is masking, and it is the single most useful idea in this chapter.

Masking is not symmetrical. A loud low frequency masks higher frequencies far more effectively than a loud high frequency masks lower ones. A boomy 120 Hz build-up does not merely add boom; it eats the clarity of everything above it. That asymmetry is why so many rooms that measure loud enough still sound muddy, and why the fix is usually subtraction.

Which gives the rule that separates engineers who improve a mix from engineers who make it louder. When something is hard to hear, take away what is covering it before you add to it. Boosting the victim raises the whole level, brings its own masking, and moves the system closer to feedback and to the limiter. Cutting the offender costs nothing and buys headroom.

Masking also explains why a busy mix loses detail faster than a sparse one. Two instruments occupying the same narrow band do not sum to twice the interest; they compete, and the louder one wins. Arranging sources so they occupy different bands — by choice of instrument, by microphone placement, by a small cut rather than a large boost — is the audible version of giving each one room.

The band that carries meaning

Speech divides its labour. Vowels carry almost all of the energy and sit low, broadly between 250 Hz and 1 kHz. Consonants carry almost all of the meaning and sit high, broadly between 2 and 4 kHz, and they are much quieter than the vowels around them.

That is why a system can be measurably loud and still fail. Level is set by the vowels. Intelligibility is set by the consonants. Turn up a system whose 2 to 4 kHz is being masked and you get a louder mumble, which is exactly the complaint that arrives as "we cannot hear them" from a room already at 90 dB.

Three things attack that band in practice, and all three are ordinary. Low-frequency build-up in the room masks it from below. Reverberation smears the consonant into the vowel that follows it. And a microphone too far from the mouth lowers the direct-to-reverberant ratio, which does both of those at once.

So when a client says "louder", listen to what actually fails. If words are missing rather than quiet, level is the wrong control. Move the microphone closer, cut the low-mid build-up, and the same system gets clearer without getting louder — which the room, the limiter and everybody's ears will all prefer.

Damage is a dose, not a volume

Hearing loss is not caused by a moment of loudness; it is caused by energy over time. The exposure limits used in most jurisdictions work on that basis: a permitted level for a working day, halving the permitted time for every 3 dB above it, because 3 dB is double the power.

Practically, if 85 dBA is the limit for eight hours, 88 dBA is four, 91 dBA is two, and 100 dBA is about a quarter of an hour. A single loud show is a large fraction of a week's safe dose, and the dose accumulates whether or not anything hurt at the time.

The warning sign most people do meet is temporary: sounds seem dull after a show, or there is a ringing that fades by morning. That is a temporary threshold shift, and it is not a near miss — it is evidence of damage that mostly recovered. Repeated, it stops mostly recovering.

None of this comes back. There is no rest day that restores lost hair cells and no exercise that rebuilds them. The equipment that prevents it costs less than a microphone and fits in a pocket, and good moulded plugs attenuate fairly evenly across the spectrum, so the mix still sounds like the mix. Wear them for load-in and soundcheck at minimum, which is where the pointless dose is.

Equal loudness, and why a mix changes when you turn it down

The ear is not a measuring instrument with a flat response. Its sensitivity varies with frequency, and -- this is the part that matters -- the SHAPE of that variation changes with level. That single fact explains a thing every engineer notices and most blame on the equipment.

AN EQUAL-LOUDNESS CONTOUR maps, across the spectrum, the sound pressure levels that a listener perceives as equally loud. The unit is the PHON, defined against a 1 kHz reference: a tone at 40 phon is one that sounds as loud as a 1 kHz tone at 40 dB SPL, whatever its own level actually is.

THE ORIGINAL WORK IS FLETCHER AND MUNSON, 1933, who compared a test tone against a fixed 1 kHz reference set in ten-decibel steps from 0 to 120. Their name is still what people say, and their curves have been superseded: the definitive modern set is ISO 226, drawn from later measurements made in several countries and revised since.

THE CONTOURS ARE NOT FLAT AND NOT PARALLEL, and both facts are the useful part. The ear is markedly less sensitive to low frequencies at quiet levels than at loud ones, and the curves FLATTEN as level rises. So the same signal played quieter loses its apparent bass first, and gains it back as you turn it up -- without a single thing changing in the signal.

WHICH GIVES YOU THE ANSWER to a familiar complaint. A mix that sounded full in rehearsal and thin at background level has not changed; your ears have. A system that seems to gain weight as the room fills and the level comes up is doing the same thing in reverse.

SO JUDGE THE BALANCE AT THE LEVEL THE AUDIENCE WILL HEAR IT. That is the practical rule, and the reason it matters is that adding low end to fix a quiet mix produces a loud mix that is muddy -- you corrected for a property of hearing by changing the signal, and the correction is wrong at every other level.

The numbers behind hearing

These are the figures worth carrying. They are approximate by nature — hearing varies between people and declines with age — but the relationships hold for everyone.

What the curve does to a mix

• Balance judged quietly and played loud sounds bass-heavy and harsh; balance judged loud and played quietly sounds thin and nasal. Judge at the level the show will run at.
• Level flatters. If a change only sounds better when it is also louder, match the levels and listen again — most of the time the improvement disappears.
• A 1 dB move is inaudible on its own and can still matter as part of a chain of them. Do not chase what you cannot hear in isolation.

Masking, applied

• Low frequencies mask high frequencies far more than the reverse. Boom is not just boom; it is lost clarity across the whole top.
• Cut what covers rather than boost what is covered. Cutting costs no headroom, gains gain-before-feedback, and does not push the limiter.
• Two sources in the same narrow band compete instead of combining. Separate them by placement or by a small cut before reaching for level.

On the job

A corporate keynote in a ballroom for four hundred. The presenter is on a lectern microphone, the system is a pair of mains on sticks with delays halfway back, and forty minutes in the client's event manager arrives at front of house and says the back of the room cannot hear.

The meter says 88 dBA at the mix position, which is a great deal for a keynote. The instinct is to add a few decibels and make the complaint go away. Do not.

Walk to the back and listen to what is actually failing. If the level is there but the words are not — if you can hear that a person is speaking and not what they are saying — the problem is intelligibility and level is the wrong control. Adding will make a louder mumble, push the room closer to feedback, and give the front rows a worse show to fix a complaint from the back.

What is nearly always happening is one of three things, and all three are cheap to test. The presenter has drifted off the microphone, so the direct sound has fallen and the room's contribution has risen. The room has a low-mid build-up masking the consonants from below. Or the delays are not doing their job, so the back is hearing the mains late and smeared rather than reinforced.

Move the microphone, cut the build-up, check the delay. The system gets clearer without getting louder, and the room thanks you for it.

How to do it

How to judge a mix with ears you cannot recalibrate. Do this in order; each step removes a way of fooling yourself.

1. Set the level to what the show will actually run at before judging any tone. Tone decisions made at the wrong level are decisions about the wrong system.
2. Listen from where the audience is, not only from the mix position. Front of house is one seat and often the best one in the room.
3. When something is hard to hear, find what is covering it before you add to it. Sweep for the offender and cut narrowly.
4. Match levels before comparing any two settings. If a change is louder it will sound better whether or not it is better.
5. Check the top of the range against something you know. A familiar recording tells you more about a system in twenty seconds than a sweep does.
6. Listen for consonants specifically, not for loudness. If you can hear that someone is talking but not what they said, the fix is clarity.
7. Take your ears out of the room at intervals. Fatigue is real, it arrives quietly, and every decision after it is worse than the ones before.
8. Wear protection during load-in and soundcheck. That is the pointless part of the daily dose and it is entirely avoidable.

What goes wrong

Practice it

Reason these through before checking. They are all about the difference between what a meter says and what a person hears.

How Sound Travels Through a Space

A room is not a container for sound. It is part of the signal path.

Speed, temperature and air

The speed of sound in air is about 343 metres per second at 20 degrees Celsius, and it changes with temperature by roughly 0.6 metres per second per degree. A hall at 15 degrees in the morning and 25 degrees once an audience is in it has a measurably different speed of sound, which shifts the alignment of any delay you set. On large systems in changing conditions this is a real effect and one reason alignment is checked again before doors.

Air also absorbs sound, and it absorbs high frequencies far more than low ones. Over tens of metres this is significant: distant sound is not merely quieter, it is duller. Humidity changes the amount. It is why a system that sounds bright at the mix position can sound dull at the back of a large room even when the level is correct, and why the fix is high-frequency compensation on the far zones rather than simply more level.

Meeting a surface

When a travelling wave meets a surface, its energy divides three ways. Some reflects, some is absorbed by the material and turned into a tiny amount of heat, and some transmits through into whatever is on the other side. The proportions depend on the material and, critically, on frequency. Heavy, dense, sealed constructions reflect low frequencies well. Soft, porous materials absorb high frequencies well and thin ones barely touch bass at all, which is why a room draped in curtains can still be boomy.

Reflections are not inherently bad; they are most of what makes a room sound like a room. They become a problem when a reflection arrives late enough and loud enough to be heard as a separate event, or when reflections between parallel surfaces reinforce particular frequencies. A wave bouncing between two walls a fixed distance apart will reinforce itself at frequencies whose half-wavelength divides evenly into that distance, producing standing waves — places in the room where a note is much louder or almost absent. This is why bass response changes as you walk around, and why the mix position matters.

Diffraction, or what sound bends around

Light does not go round corners and sound does, which is the single most useful difference between them and the one that explains a great deal of a working day.

A wave bends around an obstacle when the obstacle is small compared with its wavelength, and is blocked by it when the obstacle is large. Because wavelength changes so enormously across the audible range, the same object is both. A 60 hertz wave is nearly six metres long, so a person, a pillar or a low barrier is a pebble in a river to it — it closes back up behind and carries on as though nothing happened. A 10,000 hertz wave is three and a half centimetres, so that same person is a wall, and there is a real shadow behind them.

Once you have seen it, you see it everywhere. It is why you can hear a conversation through an open doorway you cannot see through, and why what arrives is muffled rather than quiet: the low end diffracts around the frame and the high end does not. It is why a barrier around a generator takes the whine out and leaves the rumble. It is why a person standing between a loudspeaker and a microphone changes the sound but does not stop it, and why the change is a loss of clarity rather than a loss of level.

It is also why low frequency escapes a room that high frequency cannot. A closed door stops the consonants and passes the bass, which is exactly what you hear standing in the corridor outside a ballroom, and why a noise complaint from the room next door is always about the kick drum.

The working rule is short: an obstacle only blocks what is shorter than itself. If you want to know whether something will act as a barrier, compare its size with the wavelength you are worried about, and if the wavelength is longer, the barrier is not there.

What a surface does, and how deep a room's problems go

Energy arriving at a surface divides three ways, and the proportions depend heavily on frequency. These are the figures behind why some treatments work and others are decoration.

Standing waves, in numbers

• Between two parallel surfaces, the lowest reinforced frequency is the speed of sound divided by twice the distance.
• A room 8 metres across therefore has its first mode at about 21 Hz, with more at every multiple.
• Those modes make some positions much louder and others much quieter at particular frequencies, which is why bass changes as you walk.
• Non-parallel surfaces, or broken ones, spread the effect instead of concentrating it.

Distance and air

• Air absorbs high frequencies far more than low. Over 30 metres the difference is clearly audible.
• Humidity changes the amount, which is why an outdoor show can sound different in the evening than it did in the afternoon.
• Distant zones need high-frequency compensation rather than simply more level.

On the job

A corporate client has booked a glass-walled atrium for a presentation. You arrive to find a hard floor, glass on two sides, a high ceiling and almost nothing soft in the room. Speech from the lectern is comprehensible standing next to it and close to useless twenty metres away — not quiet, but smeared, every word overlapping the one before.

Nothing is wrong with the system. The room is returning almost all of the energy you put into it. Direct sound reaches the back of the room once; reflected sound reaches it many times over the following second, and the brain cannot separate them.

The fixes available are all geometric rather than electronic. Get the sound closer to the people, with more speakers at lower level rather than fewer at high level. Aim what you have at the audience and away from the glass. Accept less low end, because clarity in this room is worth more than weight. And say clearly, early, that the room is the constraint, so that nobody spends the afternoon looking for a fault in the rig.

How to do it

1. Walk the room before anything comes off the truck, and clap once in the middle. Listen to how long it takes to die away.
2. Identify the hard parallel surfaces and note where they point.
3. Plan coverage that puts sound on the audience and as little as possible on glass, stone and bare walls.
4. Prefer more sources at lower level over fewer at high level, because it lowers the total energy fed into the room.
5. Set delay times using the actual distance and the actual temperature, not the drawing.
6. Re-check after the room is dressed and once an audience is in it.

What goes wrong

Practice it

Answer before checking.

Reverberation and the Room's Own Voice

A room is not a container that sound sits inside. It is part of the signal path, and on most jobs it contributes more to what the audience hears than any processing decision you will make. The previous chapter dealt with a single surface. This one deals with all of them at once, and with the thing they produce together.

What reverberation actually is

Stop a sound in a room and it does not stop. Energy that has already left the source keeps bouncing between the surfaces, arriving later and later and quieter and quieter, until it falls below what you can hear. That tail is reverberation, and it is the sum of thousands of reflections too closely spaced to hear separately.

It is measured as RT60: the time taken for the sound to fall by 60 decibels after the source stops. Sixty decibels is a factor of a million in power, so RT60 is roughly the time from "loud" to "gone".

The number depends on two things and nothing else that matters. How big the room is, because a bigger room means longer gaps between reflections and more distance travelled. And how absorbent its surfaces are, because every bounce loses whatever that surface takes. A big absorbent room and a small hard room can have the same RT60 by different routes.

This is why the same system sounds like a different system in two venues. A ballroom with carpet, drapes and four hundred bodies might come in around a second. The same room with a hard floor, no drape and forty people can be two or more. Nothing in the rack changed; the last stage of the signal path did.

Critical distance, and why it decides everything

At any point in a room you are hearing two things: the direct sound that came straight from the source, and the reverberant sound that has bounced. Direct sound obeys the inverse square law and falls 6 dB per doubling of distance. The reverberant field, once you are away from the source, is roughly the same level everywhere in the room.

So there is a distance at which the two are equal. Closer than that, direct sound dominates and the source sounds clear. Further than that, the room dominates and clarity stops improving no matter what you do. That distance has a name — critical distance — and it is the most useful idea in room acoustics for someone who is not an acoustician.

Two consequences follow, and both are practical. First, inside critical distance, moving closer helps enormously; outside it, moving closer barely helps at all, because you are mostly hearing the room. Second, this is exactly why a system that is loud enough can still fail at the back: every seat beyond critical distance hears mostly reverberation, and reverberation carries level without carrying detail.

It also explains why microphone distance matters so much more than it seems it should. A lectern microphone at 15 cm is deep inside critical distance and hears almost entirely direct sound. The same microphone at 60 cm hears four times less direct sound and exactly as much room, and the difference is not subtle: it is the difference between a clear presenter and a hollow one.

Loud and unintelligible

Reverberation destroys speech by smearing it in time. A consonant is short and quiet; the vowel before it is long and loud. If the room holds the vowel for half a second, that tail arrives on top of the consonant and masks it, and the listener loses the word rather than the volume.

This is why intelligibility falls as RT60 rises, and why the effect is worst exactly where you would least want it. Long reverberation times mostly come from hard, large rooms — gymnasia, atria, churches, warehouses — which are also the rooms where events get put because they are big.

The measurements that describe this are worth recognising even if you never take one. STI, the speech transmission index, runs from 0 to 1, and about 0.6 is the boundary between comfortable and hard work. Its cousin %ALcons measures the percentage of consonants lost, where roughly 10 percent is the practical limit.

What matters for a technician is the relationship, not the number. Anything that raises the direct sound relative to the reverberant sound raises intelligibility: closer microphones, tighter loudspeaker coverage, more sources closer to the listeners, and any absorption you can persuade the venue to leave in the room. Anything that raises overall level raises both equally and changes nothing.

What you can change on a show day

You will almost never be allowed to treat a room, and you will often be told the drapes are coming down for the photographs. That is not the end of the conversation, because the direct-to-reverberant ratio has more than one input and most of them are yours.

Coverage is the biggest. A loudspeaker aimed at the audience puts its energy into people, who absorb it. The same loudspeaker aimed over their heads puts the same energy into the back wall, which returns it to the room. Aiming is free and it is the single most effective acoustic tool on a normal job.

Distance is the second. More, smaller sources closer to the listeners beat fewer, louder sources further away, every time, in a reverberant room. That is the entire argument for delay speakers, and it is an acoustics argument rather than a level one.

Then there is the room's own furniture. An audience is an excellent absorber, so a room measured empty will sound different full — plan for it rather than be surprised. Drape, carpet, seating, and anything soft that is already there all help, and the polite request to leave a drape in place is worth making early, when it is a conversation rather than an interruption.

Where RT60 comes from

This book uses RT60 -- the time for sound to decay by sixty decibels -- as the number that describes a room. It is worth seeing where it comes from, because the equation says something useful even to somebody who will never calculate one.

WALLACE CLEMENT SABINE derived it at Harvard in 1898, and it is the equation that started architectural acoustics as a field:

T60 = 0.161 x V / A

V is the room's volume in cubic metres. A is the TOTAL ABSORPTION, in units called sabins, which is the sum across every surface of that surface's absorption coefficient times its area. The constant carries units of seconds per metre and comes from the speed of sound together with the logarithmic relationship between intensity and decibels.

READ IT AS A RELATIONSHIP rather than as arithmetic and it tells you two things worth carrying.

REVERBERATION SCALES WITH VOLUME. A bigger room rings longer for the same treatment, which is why a sports hall is difficult and a small studio is not, and why making a room larger makes it acoustically worse unless you also make it more absorbent.

AND IT SCALES INVERSELY WITH TOTAL ABSORPTION -- where absorption is coefficient TIMES AREA. So a small amount of very absorbent material and a large amount of slightly absorbent material can be worth exactly the same. An audience is a large area of quite absorbent material, which is the measured reason a room full of people is a different acoustic space from the same room empty.

AND THE EQUATION HAS LIMITS, which are usually left out when it is quoted. Sabine assumed a diffuse field with absorption spread reasonably evenly. In a very absorbent room, or one where all the absorption is on a single surface, it over-predicts the reverberation time, and other formulations are used instead. A number from this equation is a good estimate of a room, not a measurement of it.

Absorption is not the only tool

The instinct when a room sounds wrong is to add absorption, and it is only half the available answer.

ABSORPTION REMOVES ENERGY. Sound arrives at the material, some of it is converted to heat, and less comes back. That is what lowers RT60 and it is what the Sabine equation counts.

DIFFUSION SCATTERS IT. A diffusing surface takes one strong reflection and returns many weaker ones, spread across directions and arrival times. The energy is still in the room; what has gone is the single loud arrival from one direction.

THE DIFFERENCE DECIDES WHAT A ROOM FEELS LIKE. Kill a slap echo with absorption and you have removed that reflection and some of everything else with it -- do enough of that and the room goes quiet and lifeless, which people describe as dead or airless. Scatter the same reflection instead and the problem goes while the room keeps its sense of space.

WHICH IS WHY GOOD ROOMS USE BOTH, and usually in different places: absorption where a specific reflection has to go, at first reflection points and in corners where low frequencies build; diffusion across large parallel surfaces where the problem is repetition rather than energy.

The numbers behind a room

Rough figures, and the relationships between them. Rooms vary enormously, so treat these as the shape of the thing rather than as specifications.

The ratio, not the level

• Direct sound falls 6 dB per doubling of distance. The reverberant field is roughly constant across the room. Only their ratio changes with distance.
• Inside critical distance, moving closer helps a great deal. Outside it, moving closer barely helps, because you are mostly hearing the room.
• Turning the system up raises direct and reverberant together and improves nothing. Only changing the ratio improves clarity.

What actually moves the ratio

• Aim. Energy into an audience is absorbed; energy over their heads comes back as reverberation. Aiming costs nothing.
• More sources, closer, rather than fewer and louder. This is what delay speakers are for, and the reason is acoustics rather than level.
• Microphone distance. Halving the distance from a talker doubles the direct sound and leaves the room's contribution untouched.
• Bodies. A full room is markedly more absorbent than an empty one, so a system tuned to an empty room will be bright and hard once it fills.

On the job

A charity awards evening in a converted warehouse. Concrete floor, brick walls, exposed steel roof, and eight hundred people at round tables. You arrive to find the venue has vetoed the drape budget.

Clap once in the empty room and count. If the tail runs past two seconds, you already know what the show is about, and it is not level. It is whether the words survive the trip.

So the decisions change shape. The lectern gets a microphone with a tight pattern, placed close, and the presenters get briefed to stay on it. The loudspeakers get aimed down into the audience rather than out across the room, even though that costs some throw. Delay positions stop being a nice-to-have and become the main tool, because four smaller sources near the people beat two large ones at the front.

And the tuning gets a low-mid cut it would not need anywhere else, because the room is going to add its own and the two will sum.

By doors the room is a different acoustic space again: eight hundred bodies and eighty tablecloths are the absorption the venue would not pay for. Tune with that in mind, or you will spend the first ten minutes of the show taking out the brightness you added to an empty warehouse.

How to do it

How to read a room before you build in it. Five minutes on arrival, and it changes every decision that follows.

1. Clap once, hard, in the middle of the empty room and listen to the tail. Under a second is easy, past two seconds means intelligibility is the job.
2. Listen to where the tail goes. A flutter between two parallel hard surfaces is a different problem from an even decay, and it is fixable by aiming.
3. Find the hard surfaces that face the audience, especially the back wall and any glass. Those are what will come back at the listeners.
4. Work out roughly where critical distance falls: talk at a normal level and walk away until your own voice stops getting clearer. That is the boundary.
5. Decide coverage from that. Any seat beyond it needs its own nearer source, which is what a delay position is.
6. Plan the microphones for distance before anything else. A close pattern into a talker is worth more than everything in the rack.
7. Ask early about drapes, carpet and seating, while it is a conversation and not an interruption. Absorption you are given is free.
8. Remember the audience is absorption. Tune bright-of-neutral in an empty room only if you know it will fill.

What goes wrong

Practice it

Work these out before checking. Speed of sound is 343 m/s.

When Waves Meet: Phase and Interference

Two identical signals can add up to double, or cancel to nothing. The difference is timing.

Adding waves together

When two pressure waves arrive at the same point, they add. If their peaks line up, the result is larger — constructive interference. If one's peak lines up with the other's trough, they cancel — destructive interference. With two identical signals perfectly aligned the result is 6 dB louder; perfectly opposed, the result is silence. Everything in between is partial.

Phase describes where a wave is in its cycle, expressed in degrees, and it is only meaningful as a comparison between two signals. Two signals in phase reinforce; two 180 degrees out of phase cancel. A polarity inversion — swapping the two conductors of a balanced pair — flips a signal upside down at every frequency at once, which is not the same thing as a phase shift, though the words are used loosely on show floors.

Comb filtering, and why two mics on one source is risky

The interesting case is two copies of the same sound arriving with a small time difference. At frequencies where that delay equals a whole number of cycles, the copies reinforce. At frequencies where it equals a half cycle, they cancel. The result across the spectrum is a regular series of peaks and deep notches — comb filtering, named for what it looks like on an analyser.

This is why two microphones on one source often sounds thin and hollow rather than twice as good, and it is the reasoning behind the three-to-one rule: keep microphones at least three times as far from each other as they are from their source, so the unwanted copy is quiet enough not to matter. It is also what you are hearing in the overlap between two loudspeakers covering the same seats, and why aligning a delay speaker is about time rather than level. Comb filtering is not a fault in the equipment. It is arithmetic, and the only cure is to change the geometry or the timing.

Delay used on purpose, and why a distant speaker still sounds like the stage

Everything so far has treated a second arrival as a problem. It is also a tool, and this is the one place in the book where a technician uses this physics deliberately rather than working around it.

A deep room cannot be served by one loudspeaker. The people at the back are too far away, and the inverse square law is not negotiable: six decibels for every doubling of distance means the back row is dramatically quieter than the front, or the front is painfully loud. The fix is a second loudspeaker further back — a delay speaker, and the name is the whole idea.

Left alone it makes things worse. The audience under it hears that loudspeaker first, because it is nearer, and the stage second, because sound from the stage is still crossing the room at 343 metres per second. Two arrivals a few tens of milliseconds apart, the near one arriving first, and the effect is that the sound appears to come from the box above their heads rather than from the person on stage. It is disorienting in a way people cannot name; they will say it sounds wrong without being able to say why.

So you delay it. Work out how long the stage sound takes to reach that position — distance divided by 343, or roughly three milliseconds per metre — and delay the speaker by the same amount, so both arrive together. Then add a few milliseconds more.

That last part is the useful trick and it has a name: the precedence effect, sometimes the Haas effect. When two arrivals are close in time, a listener hears one sound, and locates it at whichever arrived FIRST, even when the second is somewhat louder. Delay the near speaker so the stage wins the race by ten or fifteen milliseconds, and the audience hears the sound as coming from the stage while getting most of their level from the box overhead. They are being fooled, precisely, by arithmetic.

The window is not wide. Under about thirty milliseconds the two arrivals fuse into one and the first one wins. Past forty or fifty they separate and the second is heard as an echo, which is worse than no delay speaker at all. Between them there is a band where it works, and hitting it is a measurement rather than a taste.

What a delay does across the spectrum

Two copies of one sound, separated by a small delay, reinforce at some frequencies and cancel at others. Which ones depends only on the delay, and the arithmetic is worth seeing written down.

The shape of the result

• Cancellations occur at the first frequency and then at every odd multiple of it, producing a regular comb of notches.
• Reinforcements sit between them, so the total energy is not lost, it is redistributed.
• Two equal copies perfectly aligned give +6 dB. Perfectly opposed, they give silence.
• The quieter the second copy, the shallower the notches. A copy 10 dB down causes a wobble rather than a hole.

The three-to-one rule

• Keep microphones at least three times as far from each other as each is from its source.
• That makes the unwanted copy roughly 10 dB down, which limits the damage to about 3 dB of ripple.
• It is a rule of thumb derived directly from the inverse square law, not a separate principle.

On the job

A panel of four speakers, each with their own lavalier, sitting close together on a low stage. Every microphone is open because any of them might speak. It sounds thin and slightly hollow, and no amount of EQ improves it — every filter you try makes it worse somewhere else.

Each voice is being picked up by its own microphone and, a fraction later, by the three others. Those delayed copies are only a few decibels quieter than the direct one because the panellists are sitting close together. Every open microphone is adding a comb filter to every voice, and there are twelve such paths in the room at once.

The answer is not equalisation, because the notches move as people lean and turn. It is to reduce the number of open microphones: gate them, ride them, or use an automatic mixer that opens only the one being spoken into. Halving the number of open microphones takes about 3 dB off the problem and, more importantly, stops it changing every few seconds.

How to do it

1. Count the open microphones. Every one that is not needed is adding delayed copies of everything else.
2. Apply the three-to-one rule: each microphone at least three times as far from the others as from its own source.
3. Where two sources must overlap, make one clearly dominant rather than making them equal.
4. For loudspeakers covering the same seats, measure the path difference and align the timing rather than the level.
5. Check polarity on every pair of anything before you start chasing tone.
6. If the sound changes as people move, suspect interference rather than the equipment.

What goes wrong

Practice it

Answer before checking.

Directivity: Why Coverage Is Physics

A loudspeaker does not radiate equally in all directions, and neither does a microphone listen equally in all directions. Both facts come from the same place — the size of the wave compared with the size of the device — and between them they decide who in a room hears well.

This is the last of the consequences of wavelength, and it is the one that turns up most often in a working day.

Why high frequencies are directional and low ones are not

A wave passing an object behaves in one of two ways depending on their relative size. If the wave is much larger than the object, it bends around it and carries on as if the object were not there. If the wave is much smaller, the object blocks it and casts a shadow.

A loudspeaker is an object, and the sound it makes has to leave it. At low frequencies the wavelength is far larger than the cabinet, so the sound wraps around the box and radiates in every direction, including behind. At high frequencies the wavelength is smaller than the cabinet and the horn in front of it, so the sound leaves in a beam.

The arithmetic makes it concrete. A 100 Hz wave is 3.4 metres, so a half-metre cabinet is invisible to it and the energy goes everywhere. A 10 kHz wave is 3.4 centimetres, so the same cabinet is enormous by comparison and the energy goes where it is pointed.

Two familiar things follow. Subwoofers are essentially omnidirectional, which is why their placement is about the room rather than about aiming, and why the neighbours hear the bass. And a main loudspeaker sounds dull off to the side, because the low end still reaches you and the top end does not — you are outside the beam for the frequencies that carry detail, and inside it for the ones that carry weight.

Coverage angle, and what the numbers mean

A loudspeaker's coverage is quoted as two angles, horizontal and vertical: 90 by 60, say, or 60 by 40. That number is not the angle within which you can hear it. It is the angle within which the level has fallen by no more than 6 dB from straight ahead.

Six decibels is a large drop, so the edge of the quoted pattern is already noticeably quieter and duller than the centre. Anything beyond it falls away quickly. This is why coverage overlaps are designed at the pattern edges: two boxes crossing at their 6 dB points sum back to roughly the on-axis level in the middle, which is what makes an even wash of sound across a room.

The quoted angle is also frequency dependent, whatever the specification says. A box that is 90 degrees at 2 kHz may be 40 degrees at 10 kHz and effectively 360 at 100 Hz. The consequence is that the pattern you are aiming is the midrange pattern, and the top end is narrower than you think, which is why a seat that sounds fine walking past can sound dull when you sit down in it.

For a technician the practical version is short. Aim the box so the people are inside the pattern rather than the wall. Cross patterns at their edges rather than pointing two boxes at the same seats. And check coverage by ear at the edges of the audience, not at the middle, because the middle always sounds fine.

Why one loudspeaker cannot serve a deep room

Put a single loudspeaker at the front of a long room and consider two listeners: one at 4 metres and one at 32 metres. That is three doublings of distance, so the far listener receives about 18 dB less direct sound than the near one.

To make the back row comfortable you would have to make the front row eighteen decibels louder than comfortable, which is roughly four times as loud, and unpleasant enough that people move. This is not a fixable defect of a particular loudspeaker. It is the inverse square law, and no processing changes it.

The answer is more sources, not more level. A delay speaker halfway back is much closer to the seats it serves, so it can be far quieter and still deliver more direct sound there than the mains do. Its level is set by what those seats need, and its delay is set so its sound arrives just after the sound from the front, which keeps the image at the stage rather than at the speaker beside you.

The same logic explains line arrays, which are not simply loudspeakers in a stack. A column of sources close together interferes with itself in a controlled way, producing a pattern that falls off more slowly with distance than a single box does, over the range where the column is large compared with the wavelength. It is interference used deliberately — the chapter before this one, turned into a tool.

Microphones have the same physics, backwards

A microphone's polar pattern is the same idea pointed the other way: which directions it is sensitive to. Omnidirectional hears everything equally. Cardioid hears the front and rejects the rear. Supercardioid and hypercardioid are tighter at the front and trade that for a small lobe of sensitivity directly behind.

That rear lobe is not a defect and it matters on a stage. A cardioid's deepest rejection is directly behind it; a supercardioid's is at about 125 degrees off axis. Which pattern gives more gain-before-feedback depends entirely on where the monitors are, and pointing a supercardioid's null at a wedge is a real technique rather than a specification detail.

Directional microphones also bring proximity effect: as you get close to one, the low frequencies rise, sometimes dramatically, in the last few centimetres. Omnidirectional microphones do not do this at all. That is why a presenter leaning into a lectern microphone suddenly sounds chesty, and why a singer working a handheld can use distance as a tone control.

And a pattern is only as good as its aim. A cardioid rejects what is behind it, which is only useful if the thing you want to reject is behind it. Most feedback that survives careful gain structure is a microphone pointing, however slightly, at a loudspeaker.

The numbers behind coverage

Directivity figures vary by model and by frequency, so these are shapes rather than specifications. The relationships are what to carry.

Aiming, in order of effect

• Point the box at people rather than at walls. Energy into an audience is absorbed; energy into a back wall comes back as reverberation.
• Cross patterns at their edges, not at their centres. Two boxes overlapping at their −6 dB points sum to roughly on-axis level between them.
• Check by ear at the edges of the audience and the back row. The middle always sounds fine and tells you nothing.
• Remember the top end is narrower than the quoted angle. A seat that sounds bright standing can sound dull seated.

When to add a source instead of level

• If the far seats need more than about 6 dB over the near seats to be comfortable, you need another source rather than more gain.
• A delay speaker is set by what its own seats need, not by matching the mains, and its delay keeps the image at the stage.
• More, smaller, closer beats fewer, louder, further in any room with reverberation to spare.

On the job

A product launch in a long, narrow gallery: 40 metres deep, hard floor, one presenter, three hundred standing. The plan on the paperwork is a pair of mains at the front, turned up.

Do the arithmetic before the load-in rather than after. The front of the audience stands at about 4 metres and the back at about 32. That is three doublings, about 18 dB, and there is no setting on any console that removes it. To give the back row a comfortable 75 dBA you would be putting 93 dBA into the people at the front, who will move, complain, or both.

So the answer is not a bigger pair of boxes; it is a second pair halfway down, delayed. Each serves its own third of the room at a sensible level, and the delay is set so its sound arrives just behind the front system's, which keeps the voice apparently at the stage rather than beside the listener.

Then aim. In a narrow room the vertical pattern is what matters, because the horizontal has walls close by on both sides. Tilt the boxes down into the standing audience rather than flat down the room, and the same system puts far less energy into the far wall and gets far less of it back.

None of that is a preference. It is the inverse square law and the size of a wave, and the room was going to enforce both whether or not anyone planned for them.

How to do it

How to cover a room, in the order the decisions actually depend on each other.

1. Measure or pace the room: distance from the source to the nearest listener and to the furthest. Count the doublings between them.
2. If that is more than about three doublings, plan a second source position before choosing any boxes.
3. Choose the pattern from the room's shape. A wide shallow room wants a wide box; a long narrow one wants a narrow box and a delay.
4. Aim vertically first. Vertical coverage decides the balance between the front and back of a seating block, and it is the one people forget.
5. Cross adjacent boxes at their pattern edges rather than pointing both at the middle.
6. Set delay times by distance: divide the distance between the two source positions in metres by 343 to get seconds, then add a few milliseconds so the front system arrives first.
7. Walk the room and listen at the edges and the back. The middle always sounds fine.
8. For microphones, pick the pattern from where the monitors are, then aim the null at them rather than trusting the specification.

What goes wrong

Practice it

Speed of sound is 343 m/s. Work these before checking.

Feedback: The Loop In Every Room

Everything else in this book describes what sound does. This chapter describes what it does when you accidentally give it somewhere to go round in circles.

Feedback is the most common acoustic problem on a live job and the one most often treated as a mystery — something that happens to you, fixed by turning knobs until it stops. It is not a mystery. It is a loop with a gain, and once you can name the four things in that loop you can predict it, prevent most of it, and fix the rest without guessing.

What feedback actually is

Every open microphone in a room with loudspeakers is part of a loop. The microphone hears the room, the console amplifies what it heard, the loudspeaker puts it back into the room, and the microphone hears that too. Most of the time the loop loses energy on each trip and nothing happens. Feedback is what you hear when it stops losing.

The condition is exact and worth knowing precisely, because it explains every cure. Sound leaves the loudspeaker, travels to the microphone, and arrives quieter than it left — the room and the distance took some. The console then multiplies it by whatever gain you have set. If what comes back out is quieter than what went in, the loop dies away. If it comes back out at the same level or louder, the loop sustains itself, and it will grow until something in the chain runs out of headroom. That is the ring.

Round-trip gain of one is the whole thing. Everything a technician does about feedback is an attempt to keep that number under one.

It rings at one frequency first because the loop is not equally efficient at all of them. The room reinforces some frequencies and absorbs others, the microphone is more sensitive at some angles and frequencies, the loudspeaker is not flat either, and the sum of all that has peaks. The highest peak reaches a round-trip gain of one before the rest, so that is the note you hear. Cut it and the next peak becomes the highest, which is why ringing out a system feels like a game of whack-a-mole and why it has a natural stopping point.

The four things that change the loop

There are only four terms in the loop, and every real remedy changes one of them.

Distance from loudspeaker to microphone. The inverse square law is doing work here: doubling that distance takes about six decibels out of the loop, which is a large amount of gain bought for free. This is why the mains are in front of the performers and not behind them, and why a wedge pointed at the back of a cardioid microphone is a different proposition from one pointed at its face.

Distance from source to microphone. Moving the talker closer to the microphone raises the wanted signal without raising the loop at all, so you need less gain for the same result. A presenter who leans away from a lectern microphone has just asked you for six decibels you do not have. This is the cheapest fix in the trade and the one nobody thinks of, because it is not a knob.

Directivity. A cardioid microphone rejects what is behind it; a loudspeaker aimed away from the microphone puts less into it. Pattern is gain you did not have to spend.

And frequency response. Pulling down the exact frequency that is ringing lowers that peak below one and leaves the rest of the spectrum alone. Narrow cuts, not broad ones: a wide cut takes the ring out and takes the voice with it.

Ringing out, and why it has a limit

Ringing out a system means finding the peaks before the show does. You raise the gain slowly until the system just begins to ring, identify the frequency, cut it a little, and repeat. Each cut buys a small amount of extra gain before the next peak arrives.

It has a limit, and the limit is worth understanding rather than discovering. Every cut removes something real from the sound. The first two or three cost you almost nothing you can hear. By the sixth or seventh you are removing enough of the voice's own range that people start to say the system sounds thin, and you have bought perhaps four or five decibels of extra gain for it. If you need more than that, the answer is not another filter. It is one of the other three terms: move the microphone, move the loudspeaker, or change the pattern.

The number worth carrying is that ringing out is a few decibels, not a transformation. A system that needs fifteen more decibels before it is usable has a geometry problem, and no equaliser has ever fixed geometry.

Gain before feedback, as a working idea

Gain before feedback is the amount of level you can get out of a system, with the microphones you actually have in the positions they are actually in, before it rings. It is a property of the whole arrangement rather than of any one box, which is why it cannot be bought.

It is worth thinking about before you rig rather than after. Two open microphones instead of one costs you three decibels of it, because both are feeding the same loop; four costs six. This is the physics behind a rule you will hear stated as superstition on every job — close what you are not using — and it is why an experienced A1 mutes rather than trusts a gate.

The same arithmetic explains why a panel of six lavaliers on a small stage is difficult and a single handheld is not, and why the fix on that panel is rarely the console. It is a microphone choice and a loudspeaker position.

The numbers behind feedback

Rules of thumb, and the reasons they hold. None of them are specifications; all of them are the shape of the physics.

On the job

A panel discussion in a hotel ballroom. Four lavalier microphones, two mains either side of a low stage, and two floor wedges the client asked for so the panel can hear each other.

The room sounds fine in the walk-through with one microphone open, and starts to ring the moment the fourth panellist is unmuted, before anybody has said anything loudly. Nothing has been turned up. What changed is the number of paths into the loop: four open microphones cost about six decibels of gain before feedback compared with one, and the wedges are pointed at the panel, which means they are pointed at four microphones.

The first fix is not the equaliser. It is muting the microphones nobody is using, which on a panel means riding them rather than leaving them open. The second is the wedges — two decibels down, and angled so the dead side of each lavalier faces them, which buys back more than any filter will. Only then is it worth finding the one frequency that still rings and taking a narrow cut at it. If it needs more than a couple of those, something in the geometry is still wrong, and no amount of equalisation is going to fix a geometry problem.

How to do it

Before the room fills, in this order. The cheap fixes are all at the top, and every one of them is worth more than the equaliser.

1. Count the open microphones and close the ones nobody is speaking into. This is free gain and the largest single thing you control on a panel.
2. Get the talker as close to their microphone as the job allows. Halving that distance is about six decibels of wanted signal, and it costs the loop nothing.
3. Check what the loudspeakers are aimed at. A main pointed past the microphones, and a wedge meeting the dead side of the pattern, are worth more than any filter.
4. Raise the system gain slowly until it just begins to ring, and stop there rather than past it.
5. Find the ringing frequency and cut it narrowly — a third of an octave or less. A wide cut takes the ring out and the voice with it.
6. Raise the gain again and repeat, and stop after four or five cuts.
7. If it still is not enough, go back to positions. Feedback that survives five cuts is a geometry problem wearing an equaliser problem's clothes.

What goes wrong

Practice it

Work these out before reading the answers. Every one of them is a question you will be asked on a job, usually while somebody waits.

Where to Go Next

The physics does not change. Everything built on top of it does, which makes this the one part of an audio education that keeps paying out however far you go.

• If the room interested you most, go to acoustics and system tuning.
• If the wave behaviour interested you, go to system design and prediction software.
• If you liked reasoning about signal paths, go to Signal Flow and then Front-of-House Mixing.
• If you liked the numbers, look at measurement: dual-channel FFT is where this book's ideas become tools.
• If you liked explaining it, teach it. Nothing exposes a gap in your own understanding faster.

Whichever direction you take, the facts in this book stay underneath it. Wavelength does not stop mattering because you have moved into system design, and the inverse square law does not stop being true because you now run a department.

Choosing without guessing

Those five directions are honest but they are not a decision. What decides whether a route suits you is more ordinary than the subject matter: how much of your week is spent alone rather than in a crew, how much of it is travel, whether you would rather be measured on what you make or on whether it worked, and what you already have that you are discounting because it did not happen in AV.

Start with the Opportunity Map, at https://map.rebootav.app, which draws the whole industry as a transit map and shows what is genuinely next to the station you are standing on. For somebody holding this book that is usually closer than they think: the physics you have just learned is the entry requirement for system tech work, for RF, and for room tuning, and none of those are far from where you are. Looking around costs nothing and takes a few minutes, which is why it comes first: it is far easier to judge a route once you can see where it goes.

Then, if something on the map has your attention and you want to know whether it actually suits you, take the AV Pathfinder, at https://pathfinder.rebootav.app. It is a short personal quiz, and what comes back is three AV paths that suit you with a Reboot course journey mapped to each — the specific courses, in order, between you and that path. Not a job title and a good-luck.

Both live inside the Reboot community, which is also where the rest of the course library sits, so you will be asked to sign in.

About Reboot AV

Reboot AV exists because the audiovisual industry has a map problem. The work is there, the pay is real, and the ceiling is high, but almost nobody entering it can see the route from where they are to where they want to be. People do not fail in this trade for lack of talent. They fail because nobody showed them what the path looked like.

Reboot AV builds that map: a course library covering the full breadth of live-event and installed audiovisual work, an interactive map of the roles in the industry and the routes between them, and an assessment that helps people work out where they actually fit rather than guessing.

Glossary

What the gear actually looks like

Every device named in this book, in one place. Recognition is the whole point of Chapter 4 — use this page to attach a picture to each name before you meet it on a dock at six in the morning.

Audio

Dynamic microphone

Condenser microphone

Wireless handheld

Radio rack

Mixing console

Stage box / snake

Power amplifier

Main loudspeaker

Subwoofer

Stage monitor wedge

In-ear monitors

DI box

Video

Camera

Video switcher

Scaler / processor

Projector

LED wall panel

Confidence monitor

Lighting & control

Conventional fixture

Moving-head fixture

Lighting console

Dimmer

Show controller

Media server

Networking & infrastructure

Network switch

Patch bay

Equipment rack

Power distribution

Cable tester

A properly coiled cable

Connectors, close up

XLR

TRS / TS ¼-inch

SDI on BNC

HDMI

Cat5e / Cat6 (RJ45)

Fiber optic

DMX (5-pin XLR)

AC power — not signal