Sound

Waves

Sound is transmitted through fluids (e.g. gases, plasmas, and liquids) as longitudinal waves, also called compression waves. Through solids, however, sound can be transmitted as both longitudinal waves and transverse waves. Longitudinal sound waves are waves of alternating pressure deviations from the equilibrium pressure, causing local regions of compression and rarefaction, while transverse waves (in solids) are waves of alternating shear stress perpendicular to the direction of propagation. Unlike longitudinal sound waves, transverse sound waves have the property of polarisation.^[19]

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  Circular, longitudinal waves propagating from a source and causing particle vibration.
• 
  A longitudinal plane wave, the horizontally distorted region moving across the grid.
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  A transverse plane wave, the vertically distorted region moving across the grid.

Sound waves may be viewed using parabolic mirrors and objects that produce sound.^[20]

The energy carried by a periodic sound wave alternates between the potential energy of the extra compression (in the case of longitudinal waves) or lateral displacement strain (in the case of transverse waves) of the matter, and the kinetic energy of the particles' displacement velocity in the medium.

Although sound transmission involves many physical processes, the signal received at a point (such as a microphone or the ear) can be fully described as a time‑varying pressure. This pressure‑versus‑time waveform provides a complete representation of any sound or audio signal detected at that location.

Sound waves are often simplified as sinusoidal plane waves, which are characterized by these generic properties:

• Frequency, or its inverse, period.
• Wavelength, or its inverse, wavenumber.
• Amplitude, sound pressure or Intensity
• Speed of sound
• Direction

Sometimes speed and direction are combined as a velocity vector; wave number and direction are combined as a wave vector.

To analyse audio, a complicated waveform—such as the one shown on the right—can be represented as a linear combination of sinusoidal components of different frequencies, amplitudes, and phases.^[21][22][23]

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  Pressure‑versus‑time waveform of a 20‑millisecond clarinet tone.
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  Sinusoidal waveforms with wavelengths increasing upwards, representing pure frequency components used in Fourier analysis.

Speed

The speed of sound depends on the medium the waves pass through, and is a fundamental property of the material. The first significant effort towards measurement of the speed of sound was made by Isaac Newton. He believed the speed of sound in a particular substance was equal to the square root of the pressure acting on it divided by its density:

${\displaystyle c={\sqrt {\frac {p}{\rho }}}.}$

This was later proven wrong and the French mathematician Laplace corrected the formula by deducing that the phenomenon of sound travelling is not isothermal, as believed by Newton, but adiabatic. He added another factor to the equation—gamma—and multiplied ${\displaystyle {\sqrt {\gamma }}}$ by ${\displaystyle {\sqrt {p/\rho }}}$, thus coming up with the equation ${\displaystyle c={\sqrt {\gamma \cdot p/\rho }}}$. Since ${\displaystyle K=\gamma \cdot p}$, the final equation came up to be ${\displaystyle c={\sqrt {K/\rho }}}$, which is also known as the Newton–Laplace equation. In this equation, K is the elastic bulk modulus, c is the velocity of sound, and ${\displaystyle \rho }$ is the density. Thus, the speed of sound is proportional to the square root of the ratio of the bulk modulus of the medium to its density.

Those physical properties and the speed of sound change with ambient conditions. For example, the speed of sound in gases depends on temperature. In 20 °C (68 °F) air at sea level, the speed of sound is approximately 343 m/s (1,230 km/h; 767 mph) using the formula v [m/s] = 331 + 0.6 T [°C]. The speed of sound is also slightly sensitive, being subject to a second-order anharmonic effect, to the sound amplitude, which means there are non-linear propagation effects, such as the production of harmonics and mixed tones not present in the original sound (see parametric array). If relativistic effects are important, the speed of sound is calculated from the relativistic Euler equations.

In fresh water the speed of sound is approximately 1,482 m/s (5,335 km/h; 3,315 mph). In steel, the speed of sound is about 5,960 m/s (21,460 km/h; 13,330 mph). Sound moves the fastest in solid atomic hydrogen at about 36,000 m/s (129,600 km/h; 80,530 mph).^[25][26]

Sound pressure level

Sound pressure is the difference, in a given medium, between average local pressure and the pressure in the sound wave. A square of this difference (i.e., a square of the deviation from the equilibrium pressure) is usually averaged over time and/or space, and a square root of this average provides a root mean square (RMS) value. For example, 1 Pa RMS sound pressure (94 dBSPL) in atmospheric air implies that the actual pressure in the sound wave oscillates between (1 atm ${\displaystyle -{\sqrt {2}}}$ Pa) and (1 atm ${\displaystyle +{\sqrt {2}}}$ Pa), that is between 101323.6 and 101326.4 Pa. As the human ear can detect sounds with a wide range of amplitudes, sound pressure is often measured as a level on a logarithmic decibel scale. The sound pressure level (SPL) or L_p is defined as

${\displaystyle L_{\mathrm {p} }=10\,\log _{10}\left({\frac {{p}^{2}}{{p_{\mathrm {ref} }}^{2}}}\right)=20\,\log _{10}\left({\frac {p}{p_{\mathrm {ref} }}}\right){\mbox{ dB}}\,}$

where p is the root-mean-square sound pressure and ${\displaystyle p_{\mathrm {ref} }}$ is a reference sound pressure. Commonly used reference sound pressures, defined in the standard ANSI S1.1-1994, are 20 μPa in air and 1 μPa in water. Without a specified reference sound pressure, a value expressed in decibels cannot represent a sound pressure level.

Since the human ear does not have a flat spectral response, sound pressures are often frequency weighted so that the measured level matches perceived levels more closely. The International Electrotechnical Commission (IEC) has defined several weighting schemes. A-weighting attempts to match the response of the human ear to noise and A-weighted sound pressure levels are labeled dBA. C-weighting is used to measure peak levels.

Pitch

Pitch is perceived as how "low" or "high" a sound is and represents the cyclic, repetitive nature of the vibrations that make up sound. For simple sounds, pitch relates to the frequency of the slowest vibration in the sound (called the fundamental harmonic). In the case of complex sounds, pitch perception can vary. Sometimes individuals identify different pitches for the same sound, based on their personal experience of particular sound patterns. Selection of a particular pitch is determined by pre-conscious examination of vibrations, including their frequencies and the balance between them. Specific attention is given to recognising potential harmonics.^[36][37] Every sound is placed on a pitch continuum from low to high.

For example: white noise (random noise spread evenly across all frequencies) sounds higher in pitch than pink noise (random noise spread evenly across octaves) as white noise has more high frequency content.

Duration

Duration is perceived as how "long" or "short" a sound is and relates to onset and offset signals created by nerve responses to sounds. The duration of a sound usually lasts from the time the sound is first noticed until the sound is identified as having changed or ceased.^[38] Sometimes this is not directly related to the physical duration of a sound. For example; in a noisy environment, gapped sounds (sounds that stop and start) can sound as if they are continuous because the offset messages are missed owing to disruptions from noises in the same general bandwidth.^[39] This can be of great benefit in understanding distorted messages such as radio signals that suffer from interference, as (owing to this effect) the message is heard as if it was continuous.

Loudness

Loudness is perceived as how "loud" or "soft" a sound is, and reflects the overall pattern of auditory‑nerve activity produced by a sound. In general, louder sounds create greater displacement of the basilar membrane, which stimulates more auditory‑nerve fibres and results in a stronger neural representation of loudness.^[40]

Perceived loudness also depends on how sound energy is distributed over time. When a sound is very brief, the auditory system does not fully integrate its energy, so it is heard as softer than a longer sound presented at the same physical intensity. This process, known as temporal summation, operates over a window of roughly 200 ms.^[41] Beyond this duration, increasing the length of the sound no longer increases its perceived loudness.

The spectral complexity of a sound can also influence loudness perception. Complex tones, which activate a broader range of auditory‑nerve fibres, are often judged as louder than simple tones (such as sine waves) even when matched for physical amplitude.^[42]

Timbre

Timbre is perceived as the quality of different sounds (e.g. the thud of a fallen rock, the whir of a drill, the tone of a musical instrument or the quality of a voice) and represents the pre-conscious allocation of a sonic identity to a sound (e.g. "it's an oboe!"). This identity is based on information gained from frequency transients, noisiness, unsteadiness, perceived pitch and the spread and intensity of overtones in the sound over an extended time frame.^[21][22][23] The way a sound changes over time provides most of the information for timbre identification. Even though a small section of the wave form from each instrument looks very similar, differences in changes over time between the clarinet and the piano are evident in both loudness and harmonic content. Less noticeable are the different noises heard, such as air hisses for the clarinet and hammer strikes for the piano.

Texture

Sonic texture relates to the number of sound sources and the interaction between them.^[43][44] The word texture, in this context, relates to the cognitive separation of auditory objects.^[45] In music, texture is often referred to as the difference between unison, polyphony and homophony, but it can also relate (for example) to a busy cafe; a sound which might be referred to as cacophony.

Spatial location

Spatial location represents the cognitive placement of a sound in an environmental context; including the placement of a sound on both the horizontal and vertical plane, the distance from the sound source and the characteristics of the sonic environment.^[45][46] In a thick texture, it is possible to identify multiple sound sources using a combination of spatial location and timbre identification.

Ultrasound

Ultrasound is sound waves with frequencies higher than 20,000 Hz. Ultrasound is not different from audible sound in its physical properties, but cannot be heard by humans. Ultrasound devices operate with frequencies from 20 kHz up to several gigahertz.

Medical ultrasound is commonly used for diagnostics and treatment.

Infrasound

Infrasound is sound waves with frequencies lower than 20 Hz. Although sounds of such low frequency are too low for humans to hear as a pitch, these sound are heard as discrete pulses (like the 'popping' sound of an idling motorcycle). Whales, elephants and other animals can detect infrasound and use it to communicate. It can be used to detect volcanic eruptions and is used in some types of music.^[47]