# Sound

Sound is the vibration of matter, as perceived by the sense of hearing. Physically, sound is vibrational mechanical energy that propagates through matter as a wave.

## Perception of sound

For humans, hearing is limited to frequencies between about 20 Hz and 20000 Hz, with the upper limit generally decreasing with age. Other species have a different range of hearing. For example, dogs can perceive vibrations higher than 20 kHz. As a signal perceived by one of the major senses, sound is used by many species for detecting danger, navigation, predation, and communication. In Earth's atmosphere, water, and soil virtually any physical phenomenon, such as fire, rain, wind, surf, or earthquake, produces (and is characterized by) its unique sounds. Many species, such as frogs, birds, marine and terrestrial mammals, have also developed special organs to produce sound. In some species, these have evolved to produce song and (in humans) speech. Furthermore, humans have developed culture and technology (such as music, telephony and radio) that allows them to generate, record, transmit, and broadcast sound.

## Physics of sound

The mechanical vibrations that can be interpreted as sound can travel through all forms of matter gases, liquids, solids, and plasmas. However, sound cannot propagate through vacuum. The matter that supports the sound is called the medium.

## Longitudinal and transverse waves

Sound is transmitted through gases, plasma, and liquids as longitudinal waves, also called compression waves. Through solids, however, it can be transmitted as both longitudinal 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.

Matter in the medium is periodically displaced by a sound wave, and thus oscillates. The energy carried by the sound wave is split equally between the potential energy of the extra compression (in case of longitudinal waves) or strain (in case of transverse waves) of the matter and the kinetic energy of the oscillations of the medium.

## Sound wave properties and characteristics

Sound waves are characterized by the generic properties of waves, which are frequency, wavelength, period, amplitude, intensity, speed, and direction (sometimes speed and direction are combined as a velocity vector, or wavelength and direction are combined as a wave vector).

Transverse waves, also known as shear waves, have an additional property of polarization.

Sound characteristics can depend on the type of sound waves (longitudinal versus transverse) as well as on the physical properties of the transmission medium.

Whenever the pitch of the soundwave is affected by some kind of change, the distance between the sound wave maxima also changes, resulting in a change of frequency. When the loudness of a soundwave changes, so does the amount of compression in airwave that is travelling through it, which in turn can be defined as amplitude.

## Acoustics and noise

The scientific study of the propagation, absorption, and reflection of sound waves is called acoustics.

Noise is a term often used to refer to an unwanted sound. In science and engineering, noise is an undesirable component that obscures a wanted signal.

## Speed of sound

The speed of sound depends on the medium through which the waves are passing, and is often quoted as a fundamental property of the material. In general, the speed of sound is proportional to the square root of the ratio of the elastic modulus (stiffness) 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 air at sea level, the speed of sound is approximately 343 m/s, in fresh water 1482 m/s (both at 20 °C, or 68 °F), and in steel about 5960 m/s. The speed of sound is also slightly sensitive (a second-order effect) to the sound amplitude, which means that there are nonlinear propagation effects, such as the production of harmonics and mixed tones not present in the original sound (see parametric array).

## Sound pressure level

Sound measurements
Sound pressure p
Particle velocity v
Particle velocity level (SVL)
(Sound velocity level)
Particle displacement ξ
Sound intensity I
Sound intensity level (SIL)
Sound power Pac
Sound power level (SWL)
Sound energy density E
Sound energy flux q
Surface S
Acoustic impedance Z
Speed of sound c

Sound pressure is defined as the difference between the actual pressure (at a given point and a given time) in the medium and the average, or equilibrium, pressure of the medium at that location. 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 such average is taken to obtain a root mean square (RMS) value. For example, 1 Pa RMS sound pressure in atmospheric air implies that the actual pressure in the sound wave oscillates between (1 atm $-\sqrt{2}$ Pa) and (1 atm $+\sqrt{2}$ Pa), that is between 101323.6 and 101326.4 Pa. Such a tiny (relative to atmospheric) variation in air pressure at an audio frequency will be perceived as quite a deafening sound, and can cause hearing damage, according to the table below.

As the human ear can detect sounds with a very wide range of amplitudes, sound pressure is often measured as a level on a logarithmic decibel scale. The sound pressure level (SPL) or Lp is defined as

$L_\mathrm{p}=10\, \log_{10}\left(\frac{{p}^2}{{p_\mathrm{ref}}^2}\right) =20\, \log_{10}\left(\frac{p}{p_\mathrm{ref}}\right)\mbox{ dB}$
where p is the root-mean-square sound pressure and pref 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 will match 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.

## Examples of sound pressure and sound pressure levels

Source of sound RMS sound pressure sound pressure level
Pa dB re 20 µPa
Nuclear Weapon explosion approx 248
1883 Krakatoa eruption approx 180
rocket launch equipment acoustic tests approx. 165
threshold of pain 100 134
hearing damage during short-term effect 20 approx. 120
jet engine, 100 m distant 6–200 110–140
jackhammer, 1 m distant / discotheque 2 approx. 100
hearing damage from long-term exposure 0.6 approx. 85
traffic noise on major road, 10 m distant 0.2–0.6 80–90
moving automobile, 10 m distant 0.02–0.2 60–80
TV set – typical home level, 1 m distant 0.02 approx. 60
normal talking, 1 m distant 0.002–0.02 40–60
very calm room 0.0002–0.0006 20–30
quiet rustling leaves, calm human breathing 0.00006 10
auditory threshold at 2 kHz – undamaged human ears 0.00002 0

## Equipment for dealing with sound

Equipment for generating or using sound includes musical instruments, hearing aids, sonar systems and sound reproduction and broadcasting equipment. Many of these use electro-acoustic transducers such as microphones and loudspeakers.

## Sound measurement

• Decibel, sone, mel, phon, hertz
• Sound pressure level
• Particle velocity, acoustic velocity
• Particle displacement, particle amplitude, particle acceleration
• Sound power, acoustic power, sound power level
• Sound energy flux
• Sound intensity, acoustic intensity, sound intensity level
• Acoustic impedance, sound impedance, characteristic impedance
• Speed of sound, amplitude