3. Acoustics

This week is about acoustics, a term everyone knows yet few can define properly. We will go through the physics of sound and then look more closely at instrument acoustics and room acoustics. This is the physical signal level of the four levels of description, and it is the only one of the four where the answers do not depend on there being anyone in the room.

Defining acoustics¶

Acoustics is the study of sound and its properties. The term comes from the Greek ἀκουστικός (akoustikos), meaning “of or for hearing, ready to hear.” According to the American National Standard on acoustical terminology Acoustical Society of America, 2013, acoustics has two meanings:

1. The science of sound, encompassing its production, transmission, and effects, both biological and psychological (acoustics)
2. The qualities of a room that determine its auditory characteristics (the sub-discipline of room acoustics).

We will begin with acoustics broadly and then turn to some of its subdisciplines: room acoustics and instrument acoustics this week and electroacoustics and psychoacoustics in coming weeks. These are only a few of the many subdisciplines of acoustics. Two textbooks anchor most of what follows: the classic student resource is Rossing et al. (2002), while Howard & Angus (2017) is written for music and audio engineering students.

Figure: Lindsay’s Wheel of Acoustics, illustrating the multidisciplinary nature of acoustics (source).

Why acoustics matters for musicology, music psychology, and music technology¶

Acoustics gives all three fields their scientific footing for how sound is produced, transmitted, and perceived. In musicology, it helps us analyse the physical properties of instruments and performance spaces, which feeds into historical and cultural studies of music. In music psychology, it underpins research into how we perceive pitch, timbre, loudness, and the spatial qualities of sound, which are the building blocks of musical cognition and emotion. In music technology, it guides the design of audio equipment, recording techniques, and digital sound processing. We will get back to all of these in the coming weeks.

Cause and effect¶

At its core, acoustics describes the cause and effect of sound. Seen as a system, it forms a chain from cause to effect:

The generating and receiving mechanisms usually work through transduction, the conversion of energy from one form to another (e.g., mechanical to electrical, or vice versa). Sound first propagates through a medium such as air, water, or a solid, and is then transduced again at the point of reception, ready for further processing or perception.

Take a guitarist plucking a string (cause). The string vibrates and generates sound waves (generating mechanism). These waves travel through the air (propagation) and reach the ear, where they are transduced and processed further. We will return to the ear in the psychoacoustics chapter.

The chain can be longer. The sound of a guitar can be picked up by a microphone, which converts the waves into electrical signals (reception/transduction). Those signals are sent to effects pedals and back to a loudspeaker (with amplifier), which turns them back into sound waves (effect/transduction) so the audience can hear the music.

Sounding objects and sound-producing actions¶

The “cause” at the start of the chain deserves a closer look. Sound does not appear out of nowhere: someone or something acts on a physical object, and the object responds by vibrating. Acting on an object always produces sound. If the interaction is gentle, the result may be barely audible, but it is there if you listen carefully (or attach a contact microphone).

Jensenius (2022) calls this lawful relationship an action–sound coupling: the resultant sound follows from the acoustic properties of the sounding object and the (bio)mechanics of the sound-producing action. Given the same object and the same action, the sound will always be the same. A string plucked hard sounds louder than one plucked softly, a large drum sounds deeper than a small one, and nothing changes that. Much of this chapter is about the two halves of this relationship: how objects vibrate and resonate, and how the resulting waves travel through rooms to reach listeners.

Electro-acoustic instruments break this chain. There, the performer’s action is captured by a controller, sent to a sound engine, and only turned back into sound by a loudspeaker. The relation between action and sound is then no longer given by physics but is designed: an action–sound mapping that can be arbitrary and reprogrammed at will. Pressing a synthesiser key can trigger any sound whatsoever. We return to mappings in the electroacoustics chapter, and to the different types of sound-producing actions in the body chapter. For now, the point is that in the acoustic world this chapter describes, actions on objects are the core of how sound is created.

Nature of sound waves¶

Vibrations¶

Vibrations are the oscillatory motions of particles within a medium, and they are what generate sound waves. They can be periodic (regular and repeating, as in musical notes) or aperiodic (irregular, as in noise). Whether a vibration is periodic or not shapes the resulting sound, including its pitch and timbre. In psychoacoustics we wil treat pitch perception in depth before moving on to understanding how the concept of harmony and melody relates pitch height and harmonic structure to notation and tonal organisation. Let us start with some basic properties of sound waves.

Longitudinal and transverse waves¶

Mechanical waves travel through a medium (air, water, or a solid) by making particles vibrate. They are classified by the direction of particle motion relative to the direction the wave travels:

• Longitudinal waves: Particles oscillate parallel to the direction the wave travels. Sound waves in air are a common example.
• Transverse waves: Particles oscillate perpendicular to the direction of travel. Examples include waves on a string or surface water waves.

Frequency¶

Frequency is the number of complete oscillations, or cycles, a sound wave completes per second, measured in Hertz (Hz). It sets the audible pitch of a sound: higher frequencies sound higher, lower frequencies sound lower. It is one of the properties we lean on most when we analyse and describe sound.

The frequency of a wave is closely related to its period, the time it takes for one complete cycle to occur. The period is measured in seconds (s), while frequency counts the cycles that occur per second, measured in Hertz (Hz).

The frequency of a wave ($f$) is the reciprocal of its period ($T$), and vice versa:

For example, if a wave has a period of 0.01 seconds, its frequency is f = 1 / 0.01 = 100 Hz. If the frequency is 50 Hz, the period is T = 1 / 50 = 0.02 seconds.

Amplitude¶

A sound wave’s amplitude is what we hear as how “loud” it is. More precisely, amplitude is the maximum displacement of particles in the medium from their rest position as the wave passes. On a graph such as a sine wave, it is the peak value above and below the centre line (zero).

Higher amplitude means more energy in the wave and a louder sound; lower amplitude means a quieter one. Amplitude is typically measured in metres (for displacement), pascals (for pressure), or volts (for electrical signals).

In the plot below, each sine wave has a different amplitude. The peaks and troughs mark the maximum and minimum values, showing how amplitude relates to loudness.

Sound pressure level (SPL)¶

Sound pressure level (SPL) measures the pressure variation caused by a sound wave. It is used across acoustics, audio engineering, and environmental noise monitoring to gauge sound levels and check compliance with safety standards. SPL tells us how sound behaves in different environments and how it affects human hearing.

SPL is expressed in decibels (dB), a logarithmic unit for the ratio of two values. On a logarithmic scale, each step is a multiplication rather than an addition. An increase of 10 dB corresponds to a tenfold increase in sound intensity, and 20 dB to a hundredfold increase. This lets us represent the enormous range of sound pressures compactly, which suits us well, since human hearing also responds to sound intensity logarithmically rather than linearly.

The formula for SPL in decibels is:

where $p$ is the measured sound pressure and $p_0$ is the reference sound pressure (typically 20 μPa in air).

There are two concepts that are important for understanding how loud something sounds: the 3 dB rule and the inverse-square law.

The 3 dB rule says that adding a second identical sound source raises the SPL by about 3 dB, which is double the energy but only a slight gain in perceived loudness. If a single speaker produces 70 dB SPL at a given point, a second identical speaker playing the same signal at the same place brings it to roughly 73 dB. The sound energy doubles, giving the 3 dB increase, but the loudness we hear is only a little greater, not doubled. In the same way, two 60 dB sources combine to about 63 dB. Adding a third 60 dB source brings the total to about 64.8 dB, since three times the energy corresponds to $10\log_{10}(3) \approx 4.8$ dB. A fourth source gives about 66 dB: four times the energy is two doublings, so the level rises by $2 \times 3 = 6$ dB. Notice that each new source contributes less than the one before; it takes a doubling of the number of sources, from two to four, to add the same 3 dB as going from one to two.

You also need the inverse-square law: when the distance from a sound source doubles, the sound pressure drops to one-quarter, a 6 dB reduction in SPL. This is why sounds fall away so quickly as you move away from the source.

Figure: The inverse-square law. Left: sound spreading from a point source; the energy that passes through the ring at 1 m is spread over four times the area at 2 m. Right: the sound pressure level falls by 6 dB for every doubling of the distance, here from 80 dB at 1 m to 56 dB at 16 m.

Figure: Illustration of the Inverse-Square Law, showing how sound pressure decreases with distance (Wikipedia).

Let us consider an example to understand how the 3 dB rule and inverse-square law work together. Imagine a group of people shouting together. If one person at a fixed distance produces a sound level $L_1$, then $N$ equally strong, independent people produce

In the figure below, we consider one person shouting at 90 dB. Two people, each shouting at 90 dB, would produce a sound pressure level of 93 dB. If you have a football stadium with 50,000 people, all shouting at 90 dB, they would add up 137 dB. That is only in theory, though. We also need to take into account that these people are all spread around the stadium. Imagine instead that you are standing in the middle of the stadium, with approximately 50 metres to everyone. Then, one person shouting at 90 dB in one of the seats would be heard as 56 dB, two at 59 dB, and 50,000 as 103 dB. That is still very loud, but not as dangerous to the ear.

Figure: The blue curve shows the idealised 3 dB rule at 1 m, while the orange curve includes inverse-square distance loss at an average listening distance of 50 m, showing why the realistic stadium level is much lower.

Phase¶

Phase describes the position of a point within a wave cycle, measured in degrees or radians.

Differences in phase between waves can lead to constructive interference, where the waves reinforce each other, or destructive interference, where they cancel each other out. This is the principle used in noise-cancelling headphones, which we will get back to next week.

Beating waves¶

When two sound waves of slightly different frequencies are played together, they interfere with each other. This interference causes the amplitude of the combined wave to fluctuate up and down in a regular pattern, called a beat. The beat frequency is equal to the difference between the two original frequencies.

For example, two tones with frequencies 440 Hz and 441 Hz will cause a beat frequency of 1 Hz. You hear this as the sound getting louder and softer at this beat frequency. Similarly, two tones at 440 Hz and 442 Hz give a beat frequency of 2 Hz.

Beat frequencies are both problematic and helpful. They can cause problems when trying to create a nice-sounding speaker setup. But they are helpful when you want to tune an instrument. Guitarists, for example, often use the beat frequency to tune adjacent strings.

Complex waves¶

A complex wave is a sound wave that consists of multiple frequencies combined together, rather than a single pure tone. Most sounds we hear in everyday life, such as musical notes, speech, or environmental noises, are complex waves. Below is an example of how three different sine tones are added together to create a (slightly) complex tone.

When it comes to describing complex tones, there are three closely related terms that describe the sinusoidal components:

• Partial: any of the sinusoidal components of a complex tone, including the lowest one. This is the most general term, with no assumption about how the frequencies are related.
• Harmonic: a partial whose frequency is a whole-number multiple of the fundamental frequency (the lowest partial of a periodic tone). The fundamental is itself the first harmonic, the partial at twice the fundamental is the second harmonic, and so on.
• Overtone: any partial above the fundamental. The numbering is therefore shifted by one: the first overtone is the second harmonic.

This is somewhat confusing, because they are often used interchangeably. This table summarises the counting for a harmonic tone with fundamental frequency $f_0$:

In the table, the partial and harmonic numbers are the same. This is the case for most so-called “harmonic” instruments, such as strings, wind instruments, and the voice. For these, the partials are (very nearly) harmonic, which is why their tones have a clear pitch.

Other instruments produce inharmonic partials that are not whole-number multiples of a common fundamental: bells, gongs, drums, and xylophone bars are typical examples, and their pitch can be ambiguous or absent. Piano strings sit in between, with partials stretched slightly sharp of the harmonic series because of the stiffness of the strings.

Visualising sounds¶

There are numeours approaches to visualising sounds. Here we will look at some of them.

Time vs frequency domain¶

The two most fundamentally different ways of visualising sound can be broken down to:

• Time domain: A waveform display shows how a signal’s amplitude changes over time. This view brings out the shape, duration, and dynamics of the signal.

• Frequency domain: A spectrum plot or spectrogram shows how much of the signal sits in each frequency band. This view is the one to reach for when working with pitch, timbre, and spectral content.

The Fourier transform¶

Any complex wave can be broken down into a sum of simpler sinusoids with different frequencies, amplitudes, and phases, a process called Fourier analysis. This process is based on the Fourier transform, a mathematical operation that converts a time-domain signal into its frequency-domain representation. The technique was developed by the French mathematician Joseph Fourier (1768–1830) and underpins modern signal processing and harmonic analysis.

In practice, the fast Fourier transform (FFT) is an efficient algorithm for computing the Fourier transform, fast enough for real-time analysis of audio in music technology, acoustics, and audio engineering. The transform also runs backwards: an inverse Fourier transform turns a spectrum back into a waveform.

Spectrum and spectrogram¶

The Fourier transform lets us picture sound in the frequency domain in two main ways:

• Spectrum: A plot with frequency on the x-axis and magnitude on the y-axis. It gives a snapshot of the frequency content averaged over the whole signal, that is, which frequencies are present and how strong each one is.

• Spectrogram: A representation with time on the x-axis, frequency on the y-axis, and intensity (energy) shown by colour or brightness. It reveals how the frequency content changes over time, so you can see the temporal structure of a sound. Brighter or more intense colours mean stronger energy at a given frequency and time. This makes spectrograms a good fit for musical phrases, speech patterns, and transient events.

To see how the two relate, you can plot the spectrum rotated 90 degrees so its frequency axis lines up with the spectrogram’s. Then you can see how the spectrum summarises the whole signal while the spectrogram shows how it develops over time.

Windows¶

When computing a spectrogram, the audio signal is divided into short overlapping segments, and each segment is multiplied by a mathematical function called a window before the Fourier transform is applied. The window’s size, measured as the number of samples (individual digital measurement points) it includes, sets the fundamental trade-off of spectral analysis:

• Short window (e.g., 256–512 samples): better time resolution, so rapid changes like transients, attacks, or percussive sounds are easier to see. Frequency resolution suffers, so pitch detail is less precise.
• Long window (e.g., 2048–4096 samples): better frequency resolution, revealing fine pitch detail and harmonics. Time resolution suffers, so fast events blur.

No single setting is right for every sound. Percussive or speech-like signals call for shorter windows, while sustained musical tones benefit from longer ones. The figure below shows the same test signal, steady tones plus a few short clicks, analysed with three window sizes.

The window’s shape matters less than its size, but it is not arbitrary either. In music and audio analysis the Hann window is the usual default, because it performs well across the board; you will meet it as the standard setting in Sonic Visualiser, Audacity, and other audio software.

Finally, it is also worth considering whether one uses linear or logarithmic scales in the spectrum or spectrogram. On a linear frequency axis, the frequencies are evenly spaced (e.g., 100 Hz, 200 Hz, 300 Hz). This is handy for technical work, but it compresses the low frequencies and stretches out the high ones, hiding bass and mid-range detail. A logarithmic scale spaces frequencies proportionally instead (octaves: 100 Hz, 200 Hz, 400 Hz, 800 Hz). This matches human hearing and musical pitch perception, so the structure across the whole spectrum is easier to read.

The intensity (colour) scale in a spectrogram can likewise be linear or logarithmic. A logarithmic scale compresses the dynamic range so that both loud and quiet sounds stay visible, which is the standard for audio spectrograms.

Noise¶

In signal processing, noise is defined relative to a signal: the signal is the part of a sound or measurement you are interested in, and the noise is everything else. The two form a duality, captured in the signal-to-noise ratio (SNR), and what counts as noise depends entirely on what counts as signal. The traffic rumble on a field recording is noise to be filtered away in one project and the very object of study in another.

Acoustically, noise usually refers to random or unpredictable fluctuation in sound, without a clear pitch. In acoustics and audio engineering, the different types of noise are distinguished by their frequency content and how energy is spread across the spectrum. Common types include:

• White noise: Contains all frequencies at equal intensity, giving a “hissing” sound like static from a radio or TV. It is often used for sound masking and audio testing thanks to its even frequency distribution.
• Pink noise: Has equal energy per octave, so its power decreases as frequency rises. This gives it a deeper sound, like rainfall or wind, and makes it useful for audio calibration and sleep aids.
• Brownian noise (red noise): Emphasises even lower frequencies than pink noise, producing a deep rumble or distant thunder. It is generated by random walk processes and is sometimes called “red noise.”
• Blue noise: Carries more energy at higher frequencies, giving a brighter, sharper sound. Rare in nature, it is used in dithering for digital audio and image processing.
• Grey noise: Shaped so that all frequencies are perceived as equally loud, based on psychoacoustic principles. It is used in research and testing to account for the sensitivity of human hearing.

The differences show up most clearly in the spectrum, that is, the average energy at each frequency. In the figure below, the curves are aligned at 1 kHz so that their shapes can be compared directly. The slope is what gives each noise its colour: white noise is flat, pink noise falls by 3 dB per octave, brownian noise by 6 dB per octave, and blue noise rises by 3 dB per octave. Grey noise follows the inverse of a hearing sensitivity curve, boosting the regions where the ear is least sensitive. Impulse noise, on the other hand, has a flat spectrum much like white noise; what sets it apart is how its energy is distributed in time, not in frequency.

The noise types above are “constant” in the sense that their characteristics stay the same. There is also impulse noise: sudden, short bursts such as clicks, pops, or bangs. Impulse noise is common around machinery, gunshots, and electrical discharges.

Such noise types turn up in audio testing, sound masking, electronic music, and many scientific applications. Knowing the character of each one helps when designing systems for noise reduction, audio analysis, and environmental sound studies.

Note that none of this maps neatly onto how “noise” is used in musical contexts. In everyday speech, noise is unwanted sound, but what is noise to one listener can be music to another: a distorted guitar, a pounding kick drum, or the crackle of vinyl are cherished sonic qualities somewhere. There is even a whole genre of noise music, stretching from Luigi Russolo’s futurist manifesto The Art of Noises (1913) via musique concrète to artists such as Merzbow, in which the qualities engineers work to remove are the very material of the music. So keep the two senses apart: in signal processing, noise is defined relative to a signal of interest; in music, “noisiness” is an aesthetic judgement, and no sound is noise by nature.

Sound propagation¶

Sound propagation refers to how sound waves travel through different environments and interact with materials.

Medium of propagation¶

Sound needs a medium, such as air, water, or solids, to travel. The particles in these media vibrate and transmit energy from one place to another. The speed and efficiency of sound propagation depend on the medium’s properties, especially density and elasticity. Generally, sound travels faster in materials that are more elastic and have closely packed particles.

Sound moves fastest in solids (like iron or diamond) because their particles are tightly packed and transmit vibrations efficiently. For example, you can hear a distant train by placing your ear on the rail, as sound travels much faster through metal than air. Here are some examples of the speed of sound in different media:

Temperature and humidity also affect the speed of sound: warmer or more humid air generally increases it. Altitude matters too, but only indirectly, through the drop in temperature with height. The speed of sound in a gas depends on its temperature and composition, not on pressure or density on their own.

Reflection, refraction, diffraction, and absorption¶

Four physics concepts are central to how sound behaves in general, and in rooms and instruments in particular:

• Reflection: Sound waves bounce off surfaces, creating echoes and shaping acoustics. In a concert hall, hard walls and ceilings reflect sound, producing reverberation and echoes. Inside a guitar, sound waves reflect off the wooden body, reinforcing certain frequencies and contributing to the instrument’s tone.

• Refraction: When sound moves between media (e.g., air to water), its speed changes and the wave bends. Temperature gradients in a room can bend sound waves, affecting how sound travels from the stage to the audience. In wind instruments, sound waves refract as they pass through air of varying temperature or humidity inside the instrument, subtly changing pitch and timbre.

• Diffraction: Sound waves bend around obstacles and spread out after passing through openings. Sound diffracts around furniture or pillars, so you can hear someone speaking even when they are out of direct line of sight. The sound from a violin’s f-holes diffracts, helping project the instrument in all directions.

• Absorption: Materials soak up sound energy, reducing its intensity. Carpets, curtains, and acoustic panels absorb sound, cutting echoes and making rooms quieter. The type of wood or material in a drum absorbs some sound energy, affecting the instrument’s resonance and sustain.

Together these principles shape how we experience sound everywhere from open fields to concert halls, and they influence both the design and the performance of musical instruments.

Four ways sound interacts with surfaces and materials. Reflection: the wave bounces off at the same angle it arrived. Refraction: the wave bends where its speed changes. Diffraction: the wave spreads out behind an opening or obstacle. Absorption: the wave’s energy is soaked up by a porous material.

The Doppler effect¶

So far, both source and listener have been standing still. When they move relative to each other, the perceived frequency shifts: the Doppler effect. A source moving towards you compresses the wavefronts so that more of them arrive per second, raising the pitch; a source moving away stretches them, lowering it. For a source moving at speed $v_s$ and sound travelling at speed $v$, the received frequency is

with the minus sign for an approaching source and the plus sign for a receding one. The classic example is an ambulance siren, which drops in pitch the moment the vehicle passes. At 50 km/h the shift is about 4% each way, so the passing siren falls by roughly a semitone and a half in total. At walking speeds the effect is negligible, which is why we never hear it in everyday conversation.

The Doppler effect has also been put to musical use. The Leslie speaker, inseparable from the Hammond organ sound, spins its horn so that the sound source constantly moves towards and away from the listener, turning the Doppler shift into a rich vibrato. Sound designers likewise rely on the effect whenever a car, plane, or spell needs to fly convincingly past in a film or game. Like the noise discussion above, it is a reminder that a physical “artefact” in one context can be aesthetic material in another.

Room acoustics¶

Room acoustics looks at how the physical characteristics of a space shape sound quality. A room’s shape, size, and materials all affect how sound waves behave, and with them the clarity, warmth, and reverberation we hear.

Room size and shape¶

A room’s dimensions and geometry decide how sound waves reflect, interact, and form standing waves. Irregular shapes and non-parallel surfaces help reduce unwanted echoes and resonances, while rectangular rooms with parallel walls are prone to standing waves, where certain frequencies are reinforced by repeated reflections.

Standing waves form when sound waves reflect between parallel surfaces and interfere with themselves, creating regions of constructive and destructive interference. Some frequencies are amplified (peaks) and others diminished (nulls) at particular spots in the room. The effect is strongest at low frequencies and can cause uneven bass response, so some notes sound much louder or softer depending on where you stand. Treating room modes with bass traps and careful placement of speakers and listeners helps minimise these effects.

Room modes are the specific frequencies at which standing waves occur, set by the room’s dimensions (length, width, height). Each mode is a resonance frequency where sound energy builds up. Modes are categorised as axial (between two parallel surfaces), tangential (between four surfaces), and oblique (between six surfaces). Calculating room modes helps identify problem frequencies and guides acoustic treatment towards a balanced sound.

Some of you may have come across a particular phenomenon called flutter echo: rapid, repetitive echoes that bounce between hard, parallel surfaces such as bare walls or ceilings. As a sound wave reflects back and forth between them, it produces a series of closely spaced echoes that can sound like a “ping-pong” effect or a metallic ringing. Flutter echo is especially noticeable in empty rooms or corridors, and it can degrade speech intelligibility and musical clarity. Acoustic panels or diffusers are often used to break up the parallel surfaces and remove it.

In Oslo, there is an acoustic installation at one of the entrances of the National Theatre train station built around a spectacular flutter echo. Check it out next time you pass by!

Materials¶

Construction materials do much to shape the acoustic character of a room:

• Hard surfaces (glass, concrete, tile): Reflect sound waves efficiently, raising reverberation and risking echoes. They can make a space sound “live” or “bright,” but they can also cause unwanted reflections and clarity problems.
• Soft materials (carpet, curtains, upholstered furniture, acoustic panels): Absorb sound energy, especially at mid and high frequencies, reducing reverberation and echoes. They help create a “dry” or “warm” sound, improving speech intelligibility and musical detail.
• Porous materials (foam, mineral wool, fibreglass): Very effective at absorbing sound, particularly at higher frequencies. Used in acoustic panels and bass traps to control reflections and room modes.
• Dense materials (brick, stone, thick wood): Reflect low-frequency sound and can help contain sound within a space, but they may also contribute to standing waves and bass buildup.
• Diffusive surfaces (bookshelves, irregular walls, specialised diffusers): Scatter sound waves in many directions, breaking up strong reflections and preventing flutter echoes. Diffusion improves clarity and gives a more balanced listening environment.
• Windows and doors: Can transmit sound between rooms, affecting isolation and privacy. Double glazing and solid-core doors help reduce sound transmission.

Acoustic treatment¶

The shape, size, and construction of a room are hard to change once it is built, so treatment focuses on what can be added or moved. Effective treatment combines absorption, diffusion, and the strategic placement of materials:

• Absorptive panels: Usually made from foam, fibreglass, or mineral wool and mounted on walls or ceilings to absorb mid and high frequencies. They reduce reflections, reverberation, and flutter echoes, making speech and music clearer.
• Bass traps: Absorbers placed in corners or along walls to target low-frequency energy. They help control room modes and prevent the bass buildup that makes sound uneven and “boomy.”
• Diffusers: Rather than absorbing, diffusers scatter sound waves in many directions. Often made from wood or plastic with irregular surfaces or patterns, they break up strong reflections and standing waves while keeping a sense of spaciousness and natural ambience.
• Ceiling clouds: Suspended panels above listening or performance areas absorb sound from overhead, reducing ceiling reflections and improving clarity.
• Furniture arrangement: Placing bookshelves, couches, and other furnishings well can break up reflections, adding both absorption and diffusion, since soft furniture absorbs and irregular surfaces diffuse.
• Door and window seals: Seals or heavy curtains on doors and windows improve isolation, keeping unwanted noise from entering or leaving the room.
• Acoustic curtains and rugs: Thick curtains and rugs add absorption, especially in rooms with many hard surfaces, taming excess reverberation.

A balanced approach using both absorption and diffusion gives a room that is neither too “dead” nor too “live,” supporting accurate sound reproduction and comfortable listening.

Reverberation (T60)¶

Reverberation is one of the most defining acoustic properties of a room. It is the persistence of sound in a space after the source has stopped, caused by reflections from surfaces such as walls, ceilings, and floors.

Acousticians usually quantify reverberation with T60 (sometimes written RT60): the time it takes for sound to decay by 60 dB after the source stops. The ideal reverberation time depends on what the room is for. Spaces built for speech, such as lecture halls, work best with shorter reverberation times, while concert halls for symphonic music often need longer ones for a fuller sound.

• Short T60 (0.5–1 s): Good for speech and clarity, keeping echoes down and intelligibility up.
• Moderate T60 (1.5–2 s): Suits chamber music, balancing clarity and warmth.
• Long T60 (2–3 s): Favoured for orchestral and choral music, giving a full, immersive sound.

Controlling reverberation is at the heart of designing rooms with the acoustics you want, whether for recording studios, concert halls, or home listening rooms.

Clarity index and bass ratio¶

T60 says how long sound takes to die away, but not how the energy is distributed while it does. Two further measures fill that in, and you will meet them in any concert-hall report:

• Clarity (C50, C80) compares early-arriving energy with late energy. More early energy means crisper attacks and clearer detail; more late energy means a more blended, reverberant sound. C50 (a 50 ms cutoff) is used for speech, C80 (80 ms) for music.
• Bass ratio (BR) compares low-frequency reverberation with the mid range. A high BR sounds warm, or boomy; a low one sounds thin.

Neither measure is good or bad in itself. A hall built for late-Romantic orchestral repertoire and one built for spoken theatre should have different values, and both should be read alongside T60.

Instrument acoustics¶

Room acoustics is a large field, and there are plenty of jobs for people who build and modify rooms in buildings. Far fewer people work on instrument acoustics. The scale is smaller, but most of the same principles apply, now turned to how musical instruments generate, shape, and radiate sound. Rossing et al. (2002) treats each instrument family in detail.

Principles of instrument acoustics¶

The main physical principles are the vibration source and the instrument’s resonance. The initial sound comes from vibrating elements such as strings (guitar, violin), air columns (flute, trumpet), membranes (drum), or solid bodies (xylophone). Most instruments then have resonating bodies—soundboards, tubes, shells—that amplify and colour the sound. The shape, size, and material of these bodies set the instrument’s timbre and loudness.

The vibration source largely determines the frequency range of the instrument. Each instrument has a characteristic range of frequencies it can produce, fixed by its physical dimensions and construction.

Figure: Approximate ranges of fundamental frequencies for some instruments on a logarithmic axis, against the range of hearing and the range of vibration felt through the skin. The bars cover fundamentals only; the harmonics of every instrument reach far higher, which is what gives it its timbre. After a chart by Sebastian Merchel.

Resonance also shapes timbre—the sound “colour”—through the instrument’s partials and overtones. Instruments rarely produce pure tones; they generate complex waves with many harmonics, and the relative strength of those harmonics gives each instrument its distinctive sound.

An instrument’s radiation pattern describes how it projects sound into the surrounding space and depends on its geometry and on playing technique.

Organology¶

Not many people know about it, but there is a (small) academic field devoted to the study of musical instruments: organology. It was developed by (ethno)musicologists and researchers in instrument museums in the late 19th and early 20th century, out of the need to organise large collections of instruments.

The best-known organological system is the Hornbostel–Sachs System, which classifies instruments by how they produce sound. The main categories are:

• Idiophones: Instruments that produce sound mainly through the vibration of their own material, without strings, membranes, or external air columns. Examples include xylophones, cymbals, and bells.
• Membranophones: Instruments that produce sound by vibrating a stretched membrane. Drums are the most common example, where the membrane is struck, rubbed, or otherwise excited.
• Chordophones: Instruments that produce sound by vibrating strings stretched between fixed points. This group includes violins, guitars, harps, and pianos.
• Aerophones: Instruments that produce sound by vibrating columns of air. Examples are flutes, trumpets, saxophones, and pipe organs.
• Electrophones: Instruments that produce sound mainly through electrical means. This includes synthesisers, electric guitars (when amplified), and theremins.

Each category divides further by how the sound is initiated (struck, plucked, bowed, blown, and so on), by the construction of the instrument, and by its acoustic properties. On a lighter note, Disney made an animated film called Toot Whistle Plunk and Boom in 1953 that plays with the differences between instruments:

(If embedded playback is disabled for this film, watch it directly on YouTube.)

The voice¶

The Hornbostel–Sachs system was developed to categorise instruments in museums and therefore does not include the most common instrument there is: the human voice. The voice is arguably also one of the most complex of all instruments, even though its physical principles can be reduced to two basic parts: a vibration source and a resonator.

The standard description of how the voice works is the source–filter model Sundberg, 1987. The source is the pair of vocal folds in the larynx. Air pressed up from the lungs sets the folds vibrating, chopping the airflow into a rapid series of puffs. The result is a buzzing tone rich in harmonics, and the rate of vibration sets the pitch, typically around 100–150 vibrations per second in male speech and 200–250 in female speech. The filter is the vocal tract, the air-filled tube running from the larynx through the mouth and nose. Like any tube, it has resonances that amplify some harmonics and dampen others, colouring the buzz into a recognisable voice.

The resonance peaks of the vocal tract are called formants. Moving the tongue, lips, and jaw reshapes the tract and shifts the formant frequencies, and the two lowest formants are what distinguish one vowel from another. Sing the same pitch first on “ee” and then on “ah”: the vocal folds do the same thing throughout, but the changed filter moves the formants and the vowel changes. This is also why a wah-wah pedal sounds vocal, since it sweeps a resonance in much the way a mouth does.

Singing differs from speech mainly in what the source does. Speech slides quickly through pitches, while singing holds them steady and shapes loudness deliberately. Many singers also add vibrato, a regular pitch fluctuation of about five to seven cycles per second that adds warmth and helps a voice blend with or stand out from accompaniment. Because sung vowels are sustained, listeners also get more time to hear the colour of the filter.

Different styles use the instrument in strikingly different ways. Pop and rock singers often rely on belting, which carries the strong, speech-like setting of the vocal folds much higher in pitch than ordinary speech. Metal screaming and growling recruit structures above the folds to add rough distortion as a deliberate timbral effect.

Classical singers, performing without microphones, instead rely on the singer’s formant: a strong resonance peak around 2,500–3,000 Hz that arises when the third, fourth, and fifth formants are tuned close together, mainly by lowering the larynx and widening the lower throat Sundberg, 1987. The trick works because an orchestra’s energy falls off steeply in just that frequency region while the ear is near its most sensitive, so the voice rings through where the accompaniment is weakest. You hear it as the bright “ring” of an operatic voice, and it is what lets a soloist carry over a full orchestra.

A critical look: is a Stradivarius really that unique?¶

Few objects carry a reputation like a violin by Antonio Stradivari. The instruments sell for millions, soloists speak of them with reverence, and a whole literature of theories tries to explain their secret: the varnish, the density of spruce grown during the Little Ice Age, a lost craft. The claim underneath all of this is an acoustic one, and acoustic claims can be tested.

• The claim is that the old Italian instruments have a tonal quality that modern makers cannot match, and that experienced players and listeners can hear it.
• The evidence comes from a series of double-blind comparisons led by the acoustician Claudia Fritz and the violin maker Joseph Curtin. In the first, twenty-one soloists at an international competition played six violins, including two by Stradivari and one by Guarneri, and the instrument they liked best was a new one, while a Stradivari came last Fritz et al., 2012. In a larger follow-up, ten soloists spent an hour with six old and six new violins in a rehearsal room and a concert hall; they again preferred the new instruments and, asked to pick one for a hypothetical tour, most chose a modern one Fritz et al., 2014. When audiences in Paris and New York then listened to old and new instruments played in a hall, they judged the new ones to project better and preferred their sound Fritz et al., 2017. In none of the studies could players or listeners tell old from new at better than chance.
• The method is what makes the results hard to dismiss. Players wore welder’s goggles in dim light so the instruments could not be seen, the chin rests were scented so that the smell of old varnish gave nothing away, and neither the players nor the experimenters handing over the violins knew which was which.
• The limits are worth stating. Only a handful of old instruments took part, and not every famous violin is in playing condition; preference in an hour is not the same as a career-long relationship; and the studies measure sound, not the history, confidence, and prestige that a famous instrument gives the person holding it.

What survives is a lesson about instrument acoustics. The sound of a violin is the physics of a wooden box and its resonances, as this chapter has described, and modern makers understand that physics well enough to match the old masters. The rest of the legend belongs to the next chapters: expectation shapes what we hear, and knowing an instrument is a Stradivari is part of the listening.