Notes · Music TechnologyUK · A-Levels

Principles of sound and acoustics

Music technology begins with the physics of sound: what a sound wave is, how frequency and amplitude map onto the pitch and loudness we hear, and how sound behaves in a room. This topic builds the quantitative foundations - the wave equation, the audible range, the decibel and reverberation - and the psychoacoustics that explains why we hear as we do. Every later processor, from EQ to reverb, rests on these ideas, and the numeracy here (metres per second, hertz, decibels, seconds) recurs throughout the written papers.

5 sections~21 min reading time3 competenciesLevel Foundation 1 · Standard 2 · Advanced 2

T·0111 / 16

Exam profile

C3 · Describe the physical properties of sound and relate them to pitch, loudness and timbreC4 · Apply the decibel, frequency and reverberation-time relationships in production reasoningC3 · Explain how room acoustics and human hearing shape what we record and perceive

Operators:statedescribeexplaincalculatedetermine

basic level

The AS-level foundation is what a sound wave is, the audible range, the decibel as a ratio, and the idea of reverberation.

higher level

The full A-level treats these quantitatively - dB calculations, the inverse-square law, RT60 estimation and psychoacoustic effects such as masking - and applies them to production decisions.

Depth

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Contents · 5 sections

Principles of sound and acoustics

Sound as a pressure wave#

FoundationPearson 9MT0 - principles of sound and acoustics

A sound wave as pressure against time

Fig. 1A pure tone is a sine wave: the amplitude is the peak pressure change (heard as loudness) and the period is the time for one cycle (its reciprocal, the frequency, is heard as pitch).

Sound is a longitudinal pressure wave travelling through a medium: a vibrating source (a string, a cone, vocal folds) pushes and pulls on the surrounding air, creating alternating regions of slightly raised pressure (compressions) and slightly lowered pressure (rarefactions) that propagate outwards. The air molecules themselves only oscillate to and fro about a fixed point; it is the pattern of pressure, and the energy it carries, that travels. Because sound needs a medium, it cannot travel through a vacuum - a crucial difference from the electromagnetic signals that carry it once it has been converted to a voltage.

A microphone captures this pressure variation and turns it into an electrical voltage whose shape follows the pressure over time, which is why the waveform we see in a DAW is a graph of amplitude against time. The simplest sound is a sine wave - a single pure frequency - and any real, complex sound can be understood as a sum of sine waves of different frequencies and amplitudes. Reading a waveform means recognising its amplitude (the height of the oscillation, related to loudness) and its period or frequency (how quickly it repeats, related to pitch).

Three linked quantities describe any wave. The frequency f is the number of complete cycles per second, measured in hertz (Hz); the period T is the time for one cycle, so T = 1/f; and the wavelength lambda is the distance between successive compressions. In air at about 20 degrees Celsius sound travels at roughly 343 metres per second, and this speed links frequency and wavelength through the wave equation v = f*lambda. For a fixed medium the speed is essentially constant, so a higher frequency always means a shorter wavelength.

The speed of sound (~343 m/s) is far slower than the speed of light or of an electrical signal, and this has real consequences in the studio and on stage: sound takes about 3 milliseconds to travel one metre, so the distance between two microphones, or between a source and a reflecting wall, translates directly into a time delay that can cause phase problems. Holding on to the figure 'about a metre every 3 ms' (or ~343 m/s) makes many later ideas - miking distance, comb filtering, pre-delay, the Haas effect - fall into place.

Because a complex tone is a mixture of frequencies, its lowest frequency (the fundamental) fixes the perceived pitch while the higher frequencies (the harmonics or overtones) give it its characteristic tone colour or timbre. This is the single most important idea connecting the physics of sound to music: pitch, loudness and timbre are our perceptions of frequency, amplitude and the harmonic content of a wave, and every tool in music technology works by altering one of these three physical properties.

v = f\lambda, \qquad T = \dfrac{1}{f}

The wave equation and period

Wave speed equals frequency times wavelength; period is the reciprocal of frequency.

Worked example

Wavelength and period of a note

A loudspeaker reproduces a 100 Hz bass note. Taking the speed of sound in air as 343 m/s, find the wavelength of the note and its period.

Wavelength
Rearrange v = f*lambda to lambda = v/f = 343/100 = 3.43 m.
Period
T = 1/f = 1/100 = 0.010 s = 10 ms.
$T = \dfrac{1}{100} = 0.010\,\text{s} = 10\,\text{ms}$
Interpret
The 3.43 m wavelength is comparable to room dimensions, which is why low frequencies interact strongly with rooms and are hard to control acoustically.

Result: The 100 Hz note has a wavelength of about 3.4 m and a period of 10 ms.

Typical mistakes

Describing sound as a transverse wave - it is longitudinal, made of compressions and rarefactions along the direction of travel.
Confusing the period (time for one cycle) with the wavelength (distance for one cycle).

Active revision

A note has a frequency of 440 Hz. Taking the speed of sound as 343 m/s, calculate its wavelength and its period.

Active recall

Recall the key points — then reveal.

Sources: Pearson Edexcel Level 3 Advanced GCE in Music Technology (9MT0) Specification (Pearson Edexcel)

Frequency and the audible range#

StandardPearson 9MT0 - principles of sound and acoustics

The audible range on a logarithmic frequency axis

Fig. 2Frequency is drawn logarithmically: each unit is one decade (x10). The audible range 20 Hz-20 kHz spans about ten octaves, divided into the bands used in EQ and mixing.

The healthy human ear responds to frequencies between roughly 20 Hz and 20 kHz - the audible range - and pitch is our perception of frequency within it. Frequencies below 20 Hz are infrasound (felt more than heard) and above 20 kHz are ultrasound (inaudible to us). In practice the upper limit falls with age and exposure to loud sound, so many adults hear little above 15-16 kHz, but 20 Hz-20 kHz remains the working range that recording, sample rates and hearing all reference.

Pitch perception is logarithmic, not linear: what the ear hears as an equal musical step corresponds to a constant ratio of frequencies, not a constant difference. The most important ratio is the octave, a doubling of frequency: 220 Hz, 440 Hz and 880 Hz are all the note A, each an octave apart. This is why frequency is almost always drawn on a logarithmic axis in audio - on an EQ, each doubling (octave) occupies the same horizontal space, so the 20 Hz-20 kHz range spans about ten octaves.

It is useful to divide the audible range into broad bands that recur in EQ and mixing language: sub-bass (roughly 20-60 Hz), bass (60-250 Hz), low-mids (250-500 Hz), mids (500 Hz-2 kHz), high-mids or presence (2-6 kHz) and highs or 'air'/brilliance (6-20 kHz). Knowing where instruments sit - the fundamental of a kick drum around 50-100 Hz, a female voice's fundamentals around 200-400 Hz, sibilance around 5-8 kHz - lets you reason about clashes and EQ moves in the later topics.

A musical note is not a single frequency but a fundamental plus a series of harmonics at integer multiples: f, 2f, 3f, 4f and so on. The fundamental fixes the pitch, and the relative strengths of the harmonics create the timbre that distinguishes a violin from a flute playing the same note. A bright sound has strong high harmonics; a mellow sound has weak ones. This harmonic series is the basis of additive synthesis, of how filters and EQ change tone, and of why distortion (which adds harmonics) changes a sound's character.

The relationship between the fundamental and its harmonics also underlies the idea of the 'missing fundamental': the ear can perceive the pitch of a low note from its harmonics alone, even when the fundamental frequency is absent - which is how small loudspeakers and earbuds convey a bass line they cannot physically reproduce. Frequency, then, is not just a number but the axis along which pitch, timbre and every frequency-shaping tool operate.

Worked example

Octaves and harmonics of a bass note

An electric bass plays a note with a fundamental of 55 Hz. Give the frequency two octaves higher, and list the first three harmonics of the 55 Hz note.

One octave up
An octave is a doubling: 55 x 2 = 110 Hz.
Two octaves up
Double again: 110 x 2 = 220 Hz, so two octaves above 55 Hz is 220 Hz.
Harmonics
Harmonics are integer multiples of the fundamental: 1st = 55 Hz (the fundamental), 2nd = 110 Hz, 3rd = 165 Hz.
Note the overlap
The 2nd harmonic (110 Hz) is exactly one octave up, but the 3rd (165 Hz) is not a whole octave - it is an octave plus a fifth - showing why harmonics and octaves are related but not identical.

Result: Two octaves above 55 Hz is 220 Hz; the first three harmonics are 55, 110 and 165 Hz.

Typical mistakes

Treating frequency as linear - a step from 100 to 200 Hz is one octave, but 10,000 to 10,100 Hz is a tiny fraction of one.
Saying the harmonics determine the pitch; the fundamental sets the pitch, the harmonics set the timbre.

Active revision

A note has a fundamental of 110 Hz. Write down the frequencies of its first four harmonics, and state which note lies two octaves above the fundamental.

Active recall

Recall the key points — then reveal.

Sources: Pearson Edexcel Level 3 Advanced GCE in Music Technology (9MT0) Specification (Pearson Edexcel)

Amplitude, the decibel and loudness#

StandardPearson 9MT0 - principles of sound and acoustics

The dB SPL scale of everyday sounds

Fig. 3Sound pressure level in dB SPL, referenced to the 0 dB threshold of hearing. Because the scale is logarithmic, each 6 dB step is a doubling of pressure and each 10 dB step sounds roughly twice as loud.

Amplitude is the size of a wave's oscillation - the peak pressure change of a sound, or the peak voltage of the signal that represents it - and it is heard as loudness. But the ear's response to amplitude, like its response to frequency, is roughly logarithmic and spans an enormous range: the loudest sound we can tolerate carries about a million million times the power of the quietest we can hear. To handle such a range with manageable numbers, audio uses the decibel, a logarithmic unit of ratio.

The decibel expresses a ratio between two amplitudes or two powers. For a ratio of amplitudes (voltages or pressures) the level difference in decibels is 20log10(A1/A2); for a ratio of powers or intensities it is 10log10(P1/P2). The factor of 20 versus 10 arises because power is proportional to amplitude squared. The key benchmarks are worth memorising: +6 dB is a doubling of amplitude, +20 dB is a tenfold increase in amplitude, and +3 dB is a doubling of power.

The decibel is a ratio, so it needs a reference to become an absolute level. Sound in the air is measured in dB SPL (sound pressure level), referenced to 20 micropascals, the nominal threshold of hearing at 0 dB SPL. On this scale a quiet room is around 30 dB SPL, normal conversation around 60 dB SPL, a busy road around 80 dB SPL, a loud concert around 110 dB SPL, and the threshold of pain around 130 dB SPL. Because the scale is logarithmic, these modest-looking numbers represent huge differences in actual pressure and power.

As sound spreads out from a small source in the open, its energy is distributed over an expanding sphere, so the intensity falls with the square of the distance - the inverse-square law. Each doubling of distance quarters the intensity, which is a fall of 10*log10(1/4) = -6 dB in sound pressure level. This is why moving a microphone twice as far from a source drops its level by about 6 dB, and it is the physical basis of how close and distant miking change the balance of direct to reflected sound.

Loudness is the perception, and it is not identical to measured level: doubling the sound pressure (+6 dB) does not sound twice as loud, and a widely used rule of thumb is that a change of about +10 dB is needed before most listeners judge a sound to be roughly twice as loud. Perceived loudness also depends on frequency (the ear is most sensitive around 2-4 kHz) and on duration. Distinguishing physical amplitude, measured level in decibels, and perceived loudness is essential for reasoning about gain, metering and mixing later on.

L_{dB} = 20\log_{10}\!\left(\dfrac{A_1}{A_2}\right) = 10\log_{10}\!\left(\dfrac{P_1}{P_2}\right)

The decibel

Amplitude ratios use a factor of 20; power ratios use a factor of 10 (because power is proportional to amplitude squared).

Worked example

A gain in decibels and a distance change

A pre-amp increases a signal's voltage by a factor of 10. Express this as a gain in decibels. Separately, a singer moves from 0.5 m to 1.0 m from a microphone in the open air; estimate the change in captured level.

Voltage gain in dB
Amplitude ratio, so use the factor of 20: gain = 20log10(10) = 201 = 20 dB.
Doubling the distance
Going from 0.5 m to 1.0 m doubles the distance, so by the inverse-square law the level falls by about 6 dB.
Interpret
The +20 dB pre-amp gain is a tenfold rise in amplitude, while the -6 dB from doubling the distance is a halving of amplitude - the two are the arithmetic of gain and miking distance.

Result: A x10 voltage gain is +20 dB; doubling the mic distance drops the level by about 6 dB.

Typical mistakes

Using 10log10 for a voltage or pressure ratio - amplitude ratios use 20log10; only power/intensity ratios use 10*log10.
Treating the decibel as an absolute unit without a reference; dB SPL, dBu and dBFS all reference different quantities.

Active revision

A signal's amplitude is increased by a factor of 4. Express this gain in decibels. Then state the change in dB when a source is moved from 1 m to 4 m away.

Active recall

Recall the key points — then reveal.

Sources: Pearson Edexcel Level 3 Advanced GCE in Music Technology (9MT0) Specification (Pearson Edexcel) · Ofqual - GCE AS and A level qualifications (subject-level conditions and requirements) (Ofqual)

Room acoustics and reverberation (RT60)#

AdvancedPearson 9MT0 - principles of sound and acoustics

Reverberant decay and RT60

Fig. 4After the source stops, the reverberant level decays. RT60 is the time to fall by 60 dB - here 1.0 s. A steeper decay (more absorption) gives a shorter RT60.

In any real space a listener or microphone receives sound by several routes: the direct sound that travels straight from the source, then early reflections that bounce once off nearby surfaces and arrive a few milliseconds later, and finally the reverberant field - the dense, decaying wash of thousands of later reflections. The balance of direct to reverberant sound is what tells us how far away a source is and how large and 'live' the room is, and controlling that balance by microphone distance is one of the recordist's primary tools.

When a sound wave meets a surface it is partly reflected, partly absorbed (its energy converted to heat) and partly transmitted through. Hard, dense, flat surfaces (glass, tile, plaster) reflect strongly and make a room 'live' and reverberant; soft, porous materials (curtains, foam, carpet, people) absorb, especially at high frequencies, and make a room 'dead'. Each material has an absorption coefficient between 0 (perfect reflector) and 1 (perfect absorber), and acoustic treatment works by adding absorption where reflections cause problems.

Reverberation is the persistence of sound after the source stops, as the reflected energy dies away. Its standard measure is the reverberation time, RT60: the time taken for the reverberant sound level to fall by 60 dB (to one millionth of its power) after the source is silenced. A small treated studio might have an RT60 of 0.2-0.4 s; a living room around 0.5 s; a concert hall 1.5-2.5 s; a cathedral several seconds. RT60 rises with room volume and falls as absorption is added.

Sabine's equation makes this quantitative: RT60 = 0.161 * V / A, where V is the room volume in cubic metres and A is the total absorption in square-metre sabins (the sum of each surface's area times its absorption coefficient). The equation shows why big, hard rooms ring and small, soft rooms are dead, and it lets a designer predict how much absorptive material is needed to reach a target reverberation time. RT60 also varies with frequency, since absorption is frequency-dependent.

Reverberation matters to music technology in two ways. First, the room you record in is printed onto the recording, so a good live room can add richness while a bad one adds unwanted colour and spill - hence close miking and treated rooms. Second, artificial reverb (a later topic) recreates these direct, early-reflection and decaying-tail stages digitally, and understanding the acoustic original is what lets you set a reverb's pre-delay, size and decay time convincingly.

RT_{60} = \dfrac{0.161\,V}{A}

Sabine's equation

V is the room volume in cubic metres; A is the total absorption in square-metre sabins (area times absorption coefficient, summed over all surfaces).

Worked example

Estimating RT60 with Sabine's equation

A small studio measures 5 m x 4 m x 3 m (volume 60 cubic metres) and has a total absorption of 20 square-metre sabins. Estimate its reverberation time, then find the absorption needed to halve it.

Apply Sabine
RT60 = 0.161V/A = 0.16160/20 = 9.66/20 = 0.48 s.
Target half
To halve RT60 to 0.24 s, A must double (RT60 is inversely proportional to A), so A must rise from 20 to 40 square-metre sabins.
$RT_{60} = \dfrac{0.161 \times 60}{20} = 0.48\,\text{s}$
Interpret
Adding about 20 more square-metre sabins of absorption (for example soft furnishings or foam panels) would bring the room from a slightly live 0.48 s to a tighter 0.24 s.

Result: The room's RT60 is about 0.48 s; doubling the absorption to 40 sabins would halve it to about 0.24 s.

Typical mistakes

Defining RT60 as the time for the sound to become inaudible - it is specifically a 60 dB decay, a fixed, measurable ratio.
Assuming absorption is the same at all frequencies; most porous absorbers work far better on highs than on bass.

Active revision

A rehearsal room has a volume of 120 cubic metres and a total absorption of 24 square-metre sabins. Use Sabine's equation to estimate its RT60, and state one change that would shorten it.

Active recall

Recall the key points — then reveal.

Sources: Pearson Edexcel Level 3 Advanced GCE in Music Technology (9MT0) Specification (Pearson Edexcel)

Psychoacoustics: how we hear#

AdvancedPearson 9MT0 - principles of sound and acoustics

Key psychoacoustic effects

Fig. 5The main psychoacoustic effects and their production consequences - the reasons the ear must be managed, not just measured.

Psychoacoustics is the study of how the physical properties of sound translate into what we actually perceive, and it explains why the ear is not a simple, linear measuring instrument. Its findings shape almost every production decision: how loud to make things, which frequencies get heard, how we localise sound and how audio is compressed for streaming all depend on the quirks of human hearing rather than on the raw physics alone.

The ear's sensitivity varies strongly with frequency, described by the equal-loudness contours (the Fletcher-Munson curves). We are most sensitive in the 2-5 kHz region (roughly where speech consonants and much 'presence' live) and much less sensitive to very low and very high frequencies, especially at quiet levels. This is why bass seems to disappear when you turn a mix down, why a mix should be checked at a moderate level, and why the ear finds the presence region so easy to fatigue.

Frequency masking is the effect by which a loud sound makes a quieter sound at a nearby frequency inaudible - the louder tone 'masks' the softer. A loud bass guitar can hide a kick drum; a bright cymbal can mask a vocal's sibilance. Masking is why simply adding more tracks does not make everything louder and clearer, why EQ is used to carve space so each instrument occupies its own frequency region, and it is the principle that lets perceptual codecs such as MP3 discard masked detail without an obvious change in sound.

The precedence (Haas) effect governs how we localise sound in the presence of reflections: when the same sound arrives from two directions within about 5-35 ms, we perceive it as coming from the first (earliest) source and fuse the later arrival into it, rather than hearing an echo. This is why we can locate a speaker in a reflective room, and it is exploited in mixing to widen or thicken a sound with short delays without it collapsing into a discrete echo.

Two further perceptions matter. The ear resolves frequencies into overlapping critical bands, so sounds close in frequency compete within the same band (the basis of masking), while widely separated sounds do not. And pitch perception can reconstruct a 'missing fundamental' from the spacing of the harmonics, so we hear the correct low pitch even through a device that cannot reproduce the fundamental frequency. Together these effects mean that mixing and processing are really about managing perception, not just physical level and frequency.

Worked example

Reasoning about masking in a mix

In a mix, a bright acoustic guitar strummed high in the arrangement makes the lead vocal sound dull and hard to follow. Explain the psychoacoustic cause and give a solution.

Identify the mechanism
The guitar and the vocal share energy in the upper-mid/presence region (roughly 2-5 kHz), where the ear is most sensitive; the louder guitar masks the vocal in that band.
Consequence
Because masking works within critical bands, the vocal's intelligibility-carrying presence frequencies are hidden even though its overall level seems adequate.
Solution
Carve space with EQ: gently cut the guitar around 2-4 kHz (or dip it under the vocal) so the vocal's presence region is exposed; alternatively pan or arrange the two apart in the stereo field or in time.
Check
Verify at a moderate monitoring level, since the equal-loudness effect changes the balance of presence and bass with volume.

Result: The guitar masks the vocal in the shared, ear-sensitive presence band; cutting the guitar's presence frequencies (or separating them by pan/arrangement) unmasks the vocal.

Typical mistakes

Assuming two sounds at similar levels are both fully heard - masking can make the quieter one inaudible if they are close in frequency.
Confusing the Haas effect (fusing early arrivals into one perceived direction) with a discrete echo (a separately heard repeat).

Active revision

Explain why raising the level of a bass guitar in a mix can make the kick drum harder to hear, and describe one EQ or arrangement change that would resolve it.

Active recall

Recall the key points — then reveal.

Sources: Pearson Edexcel Level 3 Advanced GCE in Music Technology (9MT0) Specification (Pearson Edexcel)

References & sources

Sources

Pearson Edexcel

Pearson Edexcel Level 3 Advanced GCE in Music Technology (9MT0) Specification

Ofqual

Ofqual - GCE AS and A level qualifications (subject-level conditions and requirements)

Principles of sound and acoustics

5 sections~21 min reading time3 competenciesLevel Foundation 1 · Standard 2 · Advanced 2

Principles of sound and acoustics

Key points

Wavelength and period of a note

Key points

Octaves and harmonics of a bass note

Key points

A gain in decibels and a distance change

Key points

Estimating RT60 with Sabine's equation

Key points

Reasoning about masking in a mix

Sources

Principles of sound and acoustics

Key points

Wavelength and period of a note

Key points

Octaves and harmonics of a bass note

Key points

A gain in decibels and a distance change

Key points

Estimating RT60 with Sabine's equation

Key points

Reasoning about masking in a mix

Sources