- Speed of sound
Sound is a vibration that travels through an elastic medium as awave . The speed of sound describes how much distance such a wave travels in a certain amount of time. InSI Units with dry air at 20 °C (68 °F), the speed of sound is 343 m/s. This also equates to 1235 km/h, 767 mph, 1125 ft/s. At such speeds, sound can travel a mile in approximately five seconds. Although it is commonly used to refer specifically to air, the speed of sound can be measured in virtually any substance. Sound travels faster in liquids and non-porous solids than it does in air.**Basic concept**The transmission of sound can be illustrated by using a

toy model consisting of an array of balls interconnected by springs. For real material the balls represent molecules and the springs represent the bonds between them. Sound passes through the model by compressing and expanding the springs, transmitting energy to neighboring balls, which transmit energy to "their" springs, and so on. The speed of sound through the model depends on the stiffness of the springs (stiffer springs transmit energy more quickly). Effects like dispersion and reflection can also be understood using this model.In a real material, the stiffness of the springs is called the

elastic modulus , and the mass corresponds to thedensity . All other things being equal, sound will travel more slowly in denser materials, and faster in stiffer ones. For instance, sound will travel faster in iron than uranium, and faster in hydrogen than nitrogen, due to the lower density of the first material of each set. At the same time, sound will travel faster in iron than hydrogen, because the internal bonds in a solid are much stronger than the gaseous bonds between hydrogen molecules. In general, solids will have a higher speed of sound than liquids, and liquids will have a higher speed of sound than gases.Some textbooks mistakenly state that the speed of sound increases with increasing density. This is usually illustrated by presenting data for three materials, such as air, water and steel. With only these three examples it indeed appears that speed is correlated to density, yet including only a few more examples would show this assumption to be incorrect.

**General formulae**In general, the speed of sound "c" is given by:$c\; =\; sqrt\{frac\{C\}\{\; ho$where :"C" is a coefficient of stiffness :$ho$ is the

density Thus the speed of sound increases with the stiffness of the material, and decreases with the density.For general equations of state, if classical mechanics is used, the speed of sound $c$ is given by:$c^2=frac\{partial\; p\}\{partial\; ho\}$where differentiation is taken with respect to adiabatic change.

If relativistic effects are important, the speed of sound may be calculated from the

relativistic Euler equations .In a

**non-dispersive medium**sound speed is independent of sound frequency, so the speeds of energy transport and sound propagation are the same. For audible sounds air is a non-dispersive medium. But air does contain a small amount of CO_{2}which "is" a dispersive medium, and it introduces dispersion to air at ultrasonic frequencies (> 28kHz ). [*Dean, E. A. (August 1979). [*]*http://handle.dtic.mil/100.2/ADA076060 Atmospheric Effects on the Speed of Sound,*] Technical report of Defense Technical Information CenterIn a

**dispersive medium**sound speed is a function of sound frequency. The spatial and temporal distribution of a propagating disturbance will continually change. Each frequency component propagates at its ownphase velocity , while the energy of the disturbance propagates at thegroup velocity . The same phenomenon occurs with light waves -- see optical dispersion for a description.**Dependence on the properties of the medium**The speed of sound is variable and depends mainly on the temperature and the properties of the substance through of which the wave is traveling. For example, in low

molecular weight gases, such ashelium , sound propagates faster compared to heavier gases, such asxenon . In a givenideal gas the sound speed depends only on itstemperature . At a constant temperature, the ideal gaspressure has no effect on the speed of sound, because pressure anddensity (also proportional to pressure) have equal but opposite effects on the speed of sound, and the two contributions cancel out exactly. In non-ideal gases, such as a van der Waals gas, the proportionality is not exact, and there is a slight dependence on the gas pressure, even at a constant temperature. Humidity also has a small, but measurable effect on sound speed (increase of about 0.1%-0.6%), because someoxygen andnitrogen molecules of the air are replaced by the lighter molecules ofwater .**Implications for atmospheric acoustics**In the

Earth's atmosphere , the most important factor affecting the speed of sound is thetemperature (see Details below). Since temperature and thus the speed of sound normally decrease with increasing altitude, sound is refracted upward, away from listeners on the ground, creating anacoustic shadow at some distance from the source. [*cite book*] The decrease of the sound speed with height is referred to as a negative

last = Everest

first = F.

title = The Master Handbook of Acoustics

publisher = McGraw-Hill

location = New York

year = 2001

isbn = 0071360972

pages = pp. 262-263sound speed gradient . However, in thestratosphere , the speed of sound increases with height due to heating within theozone layer , producing a positive sound speed gradient.**Practical formula for dry air**The approximate speed of sound in dry (0% humidity) air, in metres per second (

**m·s**), at temperatures near 0 °C, can be calculated from: :$c\_\{mathrm\{air\; =\; 331\{.\}3\; +\; (0\{.\}606\; cdot\; vartheta)\; mathrm\{m\; cdot\; s^\{-1,$where $vartheta$ is the temperature in degrees^{-1}Celsius (°C).This equation is derived from the first two terms of the

Taylor expansion of the following much more accurate equation::$c\_\{mathrm\{air\; =\; 331.3\; sqrt\{1+frac\{vartheta\}\{273.15\; mathrm\{m\; cdot\; s^\{-1$

The value of 331.3 m/s, which represents the 0 °C speed, is based on theoretical (and some measured) values of the

heat capacity ratio , $gamma$, as well as on the fact that at 1 atm real air is very well described by the ideal gas approximation. Commonly found values for the speed of sound at 0 °C may vary from 331.2 to 331.6 due to the assumptions made when it is calculated. If ideal gas $gamma$ is assumed to be 7/5 = 1.4 exactly, the 0 °C speed is calculated (see section below) to be 331.3 m/s, the coefficient used above.This equation is correct to a much wider temperature range, but still depends on the approximation of heat capacity ratio being independent of temperature, and will fail, particularly at higher temperatures. It gives good predictions in relatively dry, cold, low pressure conditions, such as the Earth's

stratosphere . A derivation of these equations will be given in a later section.**Details****peed in ideal gases and in air**For a gas, "K" (the bulk modulus in equations above, equivalent to C, the coefficient of stiffness in solids) is approximately given by:$K\; =\; gamma\; cdot\; p$ thus $c\; =\; sqrt\{gamma\; cdot\; \{p\; over\; ho$

Where::$gamma$ is the

adiabatic index also known as the "isentropic expansion factor". It is the ratio of specific heats of a gas at a constant-pressure to a gas at a constant-volume($C\_p/C\_v$), and arises because a classical sound wave induces an adiabatic compression, in which the heat of the compression does not have enough time to escape the pressure pulse, and thus contributes to the pressure induced by the compression.:"p" is thepressure .:"$ho$" is thedensity Using the

ideal gas law to replace $p$ with "nRT"/"V", and replacing "ρ" with "nM"/"V", the equation for an ideal gas becomes::$c\_\{mathrm\{ideal\; =\; sqrt\{gamma\; cdot\; \{p\; over\; ho\; =\; sqrt\{gamma\; cdot\; R\; cdot\; T\; over\; M\}=\; sqrt\{gamma\; cdot\; k\; cdot\; T\; over\; m\}$

where

*$c\_\{mathrm\{ideal$ is the speed of sound in an ideal gas.

*$R$ (approximately 8.3145 J·mol^{-1}·K^{-1}) is the molar gas constant. [*http://physics.nist.gov/cgi-bin/cuu/Value?r*]

*$k$ is theBoltzmann constant

*$gamma$ (gamma) is theadiabatic index (sometimes assumed 7/5 = 1.400 for diatomic molecules from kinetic theory, assuming from quantum theory a temperature range at which thermal energy is fully partitioned into rotation (rotations are fully excited), but none into vibrational modes. Gamma is actually experimentally measured over a range from 1.3991 to 1.403 at 0 degrees Celsius, for air. Gamma is assumed from kinetic theory to be exactly 5/3 = 1.6667 for monoatomic molecules such asnoble gas es).

*$T$ is the absolute temperature inkelvin s.

*$M$ is the molar mass inkilogram s per mole. The mean molar mass for dry air is about 0.0289645 kg/mol.

*$m$ is the mass of a single molecule in kilograms.This equation applies only when the sound wave is a small perturbation on the ambient condition, and the certain other noted conditions are fulfilled, as noted below. Calculated values for $c\_\{mathrm\{air$ have been found to vary slightly from experimentally determined values.U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976.]

Newton famously considered the speed of sound before most of the development of

thermodynamics and so incorrectly usedisothermal calculations instead ofadiabatic . His result was missing the factor of $gamma$ but was otherwise correct.Numerical substitution of the above values gives the ideal gas approximation of sound velocity for gases, which is accurate at relatively low gas pressures and densities (for air, this includes standard Earth sea-level conditions). Also, for diatomic gases the use of $gamma,\; =\; 1.4000$ requires that the gas exist in a temperature range high enough that rotational heat capacity is fully excited (i.e., molecular rotation is fully used as a heat energy "partition" or reservoir); but at the same time the temperature must be low enough that molecular vibrational modes contribute no heat capacity (i.e., insigificant heat goes into vibration, as all vibrational quantum modes above the minimum-energy-mode, have energies too high to be populated by a significant number of molecules at this temperature). For air, these conditions are fulfilled at room temperature, and also temperatures considerably below room temperature (see tables below). See the section on gases in

heat capacity for a more complete discussion of this phenomenon.If temperatures in degrees

Celsius (°C) are to be used to calculate air speed in the region near 273kelvin s, then Celsius temperature $vartheta\; =\; T\; -\; 273.15$ may be used.:$c\_\{mathrm\{ideal\; =\; sqrt\{gamma\; cdot\; R\; cdot\; T\}\; =\; sqrt\{gamma\; cdot\; R\; cdot\; (vartheta\; +\; 273.15)\}$

:$c\_\{mathrm\{ideal\; =\; sqrt\{gamma\; cdot\; R\; cdot\; 273.15\}\; cdot\; sqrt\{1+frac\{vartheta\}\{273.15$

For dry air, where $vartheta,$ (theta) is the temperature in degrees

Celsius (°C).Making the following numerical substitutions:$R\; =\; R\_*/M\_\{mathrm\{air$, where $R\_*\; =\; 8.315410\; cdot\; mathrm\{J\; cdot\; mol^\{-1\; cdot\; K^\{-1\}$ is the molar gas constant, $M\_\{mathrm\{air\; =\; 0.0289645\; cdot\; mathrm\{kg\; cdot\; mol^\{-1$, and using the ideal diatomic gas value of $gamma,\; =\; 1.4000$

Then:

:$c\_\{mathrm\{air\; =\; 331.3\; mathrm\{m\; cdot\; s^\{-1\; sqrt\{1+frac\{vartheta\}\{273.15$

Using the first two terms of the Taylor expansion:

:$c\_\{mathrm\{air\; =\; 331.3\; mathrm\{m\; cdot\; s^\{-1\; (1\; +\; frac\{vartheta\}\{2\; cdot\; 273.15\})\; ,$

:$c\_\{mathrm\{air\; =\; 331\{.\}3\; +\; (0\{.\}606\; cdot\; vartheta)\; mathrm\{m\; cdot\; s^\{-1,$

The derivation includes the two approximate equations which were given in the introduction. For Celsius temperatures which are negative, the second term of the equation right hand side, is negative.

**Effects due to wind shear**The speed of sound varies with temperature. Since temperature and sound velocity normally decrease with increasing altitude, sound is refracted upward, away from listeners on the ground, creating an

acoustic shadow at some distance from the source. [*cite book | last = Everest | first = F. | title = The Master Handbook of Acoustics | publisher = McGraw-Hill | location = New York | year = 2001 | isbn = 0071360972 | pages = pp. 262-263*] Wind shear of 4 m/s/km can produce refraction equal to a typical temperaturelapse rate of 7.5 °C/km. [*cite book | last = Uman | first = Martin | title = Lightning | publisher = Dover Publications | location = New York | year = 1984 | isbn = 0486645754*] Higher values of wind gradient will refract sound downward toward the surface in the downwind direction, [*cite book | last = Volland | first = Hans | title = Handbook of Atmospheric Electrodynamics | publisher = CRC Press | location = Boca Raton | year = 1995 | isbn = 0849386470 | pages = p. 22*] eliminating the acoustic shadow on the downwind side. This will increase the audibility of sounds downwind. This downwind refraction effect occurs because there is a wind gradient; the sound is not being carried along by the wind. [*cite book | last = Singal | first = S. | title = Noise Pollution and Control Strategy | publisher = Alpha Science International, Ltd | location = | year = 2005 | isbn = 1842652370 | pages = p. 7 | quote = It may be seen that refraction effects occur only because there is a wind gradient and it is not due to the result of sound being convected along by the wind.*]For sound propagation, the exponential variation of wind speed with height can be defined as follows:cite book | last = Bies | first = David | title = Engineering Noise Control; Theory and Practice | publisher = Spon Press | location = London | year = 2003 | isbn = 0415267137 | pages = p. 235 | quote = As wind speed generally increases with altitude, wind blowing towards the listener from the source will refract sound waves downwards, resulting in increased noise levels.]

:$U(h)\; =\; U(0)\; h\; ^\; zeta$

:$frac\; \{dU\}\; \{dH\}\; =\; zeta\; frac\; \{U(h)\}\; \{h\}$

where:

:$U(h)$ = speed of the wind at height $h$, and $U(0)$ is a constant :$zeta$ = exponential coefficient based on ground surface roughness, typically between 0.08 and 0.52:$frac\; \{dU\}\; \{dH\}$ = expected wind gradient at height $h$

In the 1862

American Civil War Battle of Iuka , an acoustic shadow, believed to have been enhanced by a northeast wind, kept two divisions of Union soldiers out of the battle, [*cite book | last = Cornwall | first = Sir | title = Grant as Military Commander | publisher = Barnes & Noble Inc | location = | year = 1996 | isbn = 1566199131 pages = p. 92*] because they could not hear the sounds of battle only six miles downwind. [*cite book | last = Cozzens | first = Peter | title = The Darkest Days of the War: the Battles of Iuka and Corinth | publisher = The University of North Carolina Press | location = Chapel Hill | year = 2006 | isbn = 0807857831*]**Tables**In the standard atmosphere:

"T"

_{0}is 273.15 K (= 0 °C = 32 °F), giving a theoretical value of 331.3 m·s^{-1}(= 1086.9 ft/s = 1193 km·h^{-1}= 741.1 mph = 644.0 knots). Values ranging from 331.3-331.6 may be found in reference literature, however.

"T"_{20}is 293.15 K (= 20 °C = 68 °F), giving a value of 343.2 m·s^{-1}(= 1126.0 ft/s = 1236 km·h^{-1}= 767.8 mph = 667.2 knots).

"T"_{25}is 298.15 K (= 25 °C = 77 °F), giving a value of 346.1 m·s^{-1}(= 1135.6 ft/s = 1246 km·h^{-1}= 774.3 mph = 672.8 knots).In fact, assuming an

ideal gas , the speed of sound "c" depends on temperature only,**not on the pressure**or**density**(since these change in lockstep for a given temperature and cancel out). Air is almost an ideal gas. The temperature of the air varies with altitude, giving the following variations in the speed of sound using the standard atmosphere - "actual conditions may vary".:"$vartheta$" is the temperature in °C:"c" is the speed of sound in m·s

^{-1}:"ρ" is the density in kg·m^{-3}:"Z" is the characteristicacoustic impedance in N·s·m^{-3}("Z"="ρ"·"c")Given normal atmospheric conditions, the temperature, and thus speed of sound, varies with altitude:

**Effect of frequency and gas composition**The medium in which a sound wave is travelling does not always respond adiabatically, and as a result the speed of sound can vary with frequency. [

*A B Wood, A Textbook of Sound (Bell, London, 1946)*]The limitations of the concept of speed of sound due to extreme attenuation are also of concern. The attenuation which exists at sea level for high frequencies applies to successively lower frequencies as atmospheric pressure decreases, or as the

mean free path increases. For this reason, the concept of speed of sound (except for frequencies approaching zero) progressively loses its range of applicability at high altitudes.:U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C., 1976. ]The molecular composition of the gas contributes both as the mass (M) of the molecules, and their heat capacities, and so both have an influence on speed of sound. In general, at the same molecular mass, monatomic gases have slightly higher sound speeds (over 9% higher) because they have a higher $gamma$ (5/3 = 1.66...) than diatomics do (7/5 = 1.4). Thus, at the same molecular mass, the sound speed of a monatomic gas goes up by a factor of

$\{\; c\_\{mathrm\{gas:\; monatomic\; over\; c\_\{mathrm\{gas:\; diatomic\; \}\; =\; sqrt$5 / 3} over {7 / 5 = sqrt{25 over 21} = 1.091...

This gives the 9 % difference, and would be a typical ratio for sound speeds at room temperature in

helium vs.deuterium , each with a molecular weight of 4. Sound travels faster in helium than deuterium because adiabatic compression heats helium more, since the helium molecules can store heat energy from compression only in translation, but not rotation. Thus helium molecules (monatomic molecules) travel faster in a sound wave and transmit sound faster. (Sound generally travels at about 70% of the mean molecular velocity in gases).Note that in this example we have assumed that temperature is low enough that heat capacities are not influenced by molecular vibration (see

heat capacity ). However, vibrational modes simply cause gammas which decrease toward 1, since vibration modes in a polyatomic gas gives the gas additional ways to store heat which do not affect temperature, and thus do not affect molecular velocity and sound velocity. Thus, the effect of higher temperatures and vibrational heat capacity acts to increase the difference between sound speed in monatomic vs. polyatomic molecules, with the speed remaining greater in monatomics.**Mach number**Mach number, a useful quantity in aerodynamics, is the ratio of an object's

speed to the speed of sound in the medium through which it is passing (again, usually air). At altitude, for reasons explained, Mach number is a function of temperature.Aircraft

flight instruments , however, operate using pressure differential to compute Mach number; not temperature. The assumption is that a particular pressure represents a particular altitude and, therefore, a standard temperature. Aircraft flight instruments need to operate this way because the impact pressure sensed by aPitot tube is dependent on altitude as well as speed.Assuming air to be an

ideal gas , the formula to compute Mach number in a subsonic compressible flow is derived fromBernoulli's equation for "M"<1:Olson, Wayne M. (2002). "AFFTC-TIH-99-02, "Aircraft Performance Flight Testing"." (PDF). Air Force Flight Test Center, Edwards AFB, CA, United States Air Force.]:$\{M\}=sqrt\{5left\; [left(frac\{q\_c\}\{P\}+1\; ight)^frac\{2\}\{7\}-1\; ight]\; \}$

where:$M$ is Mach number:$q\_c$ is impact pressure and :$P$ is static pressure.

The formula to compute Mach number in a supersonic compressible flow is derived from the Rayleigh Supersonic Pitot equation:

:$\{M\}=0.88128485sqrt\{left\; [left(frac\{q\_c\}\{P\}+1\; ight)left(1-frac\{1\}\{\; [7M^2]\; \}\; ight)^\{2.5\}\; ight]\; \}$

where:$M$ is Mach number:$q\_c$ is impact pressure measured behind a normal shock :$P$ is static pressure.

As can be seen, "M" appears on both sides of the equation. The easiest method to solve the supersonic "M" calculation is to enter both the subsonic and supersonic equations into a computer spread sheet such as

Microsoft Excel , OpenOffice.org Calc, or some equivalent program. First determine if "M" is indeed greater than 1.0 by calculating "M" from the subsonic equation. If "M" is greater than 1.0 at that point, then use the value of "M" from the subsonic equation as the initial condition in the supersonic equation. Then perform a simple iteration of the supersonic equation, each time using the last computed value of "M", until "M" converges to a value--usually in just a few iterations.**Experimental methods**A range of different methods exist for the measurement of sound in air.

**ingle-shot timing methods**The simplest concept is the measurement made using two

microphone s and a fast recording device such as adigital storage scope. This method uses the following idea.If a sound source and two microphones are arranged in a straight line, with the sound source at one end, then the following can be measured:

1. The distance between the microphones ("x"), called microphone basis.2. The time of arrival between the signals (delay) reaching the different microphones ("t")

Then "v" = "x" / "t"

An older method is to create a sound at one end of a field with an object that can be seen to move when it creates the sound. When the observer sees the sound-creating device act they start a stopwatch and when the observer hears the sound they stop their stopwatch. Again using "v = x" / "t" you can calculate the speed of sound. A separation of at least 200 m between the two experimental parties is required for good results with this method.

**Other methods**In these methods the

time measurement has been replaced by a measurement of the inverse of time (frequency ).Kundt's tube is an example of an experiment which can be used to measure the speed of sound in a small volume. It has the advantage of being able to measure the speed of sound in any gas. This method uses a powder to make the nodes andantinode s visible to the human eye. This is an example of a compact experimental setup.A

tuning fork can be held near the mouth of a long pipe which is dipping into a barrel ofwater . In this system it is the case that the pipe can be brought to resonance if the length of the air column in the pipe is equal to "({1+2n}λ/4)" where "n" is an integer. As the antinodal point for the pipe at the open end is slightly outside the mouth of the pipe it is best to find two or more points of resonance and then measure half a wavelength between these.Here it is the case that "v" = "fλ"

**Non-gaseous media****peed in solids**In a solid, there is a non-zero stiffness both for volumetric and shear deformations. Hence, in a solid it is possible to generate sound waves with different velocities dependent on the deformation mode. A sound wave generating volumetric deformations is called longitudinal and a transversal wave generates shear deformations. The velocities of these two different sound waves can be calculated in

isotropic solids by::$c\_\{mathrm\{long\; =\; sqrt\{frac\{E\}\{\; ho$:$c\_\{mathrm\{trans\; =\; sqrt\{frac\{G\}\{\; ho$

where

:"E" is

Young's modulus :"G" isShear modulus :"ρ" (rho) isdensity Thus in

steel the speed of longitudinal waves is approximately 5,100 m·s^{-1}. Inberyllium , a substance with relatively high stiffness and low density the speed of longitudinal waves is 12,870 m·s^{-1}. [*http://www.sizes.com/natural/sound.htm Accessed Jan 5, 2007*]In a solid with lateral dimensions much larger than the wavelength, the sound velocity is higher. It is found by replacing

Young's modulus "E" in the above formula by theplane wave modulus "M", which can be expressed in terms of theYoung's modulus andPoisson's ratio as::$M\; =\; E\; frac\{1-\; u\}\{1-\; u-2\; u^2\}$**peed in liquids**In a fluid the only non-zero stiffness is to volumetric deformation (a fluid does not sustain shear forces).

Hence the speed of sound in a fluid is given by:$c\_\{mathrm\{fluid\; =\; sqrt\; \{frac\{K\}\{\; ho$

where:"K" is the

bulk modulus of the fluid**Water**The speed of sound in water is of interest to anyone using underwater sound as a tool, whether in a laboratory, a lake or the ocean. Examples are

sonar , acoustic communication andacoustical oceanography . See [*http://www.dosits.org/ Discovery of Sound in the Sea*] for other examples of the uses of sound in the ocean(by both man and other animals). In fresh water, sound travels at about 1497 m/s at 25 °C. See [*http://www.npl.co.uk/acoustics/techguides/soundpurewater/ Technical Guides - Speed of Sound in Pure Water*] for an online calculator.**eawater**In salt water that is free of air bubbles or suspended sediment, sound travels at about 1500 m/s. The speed of sound in seawater depends on pressure (hence depth), temperature (a change of 1 °C ~ 4 m/s), and

salinity (achange of 1‰ ~ 1 m/s), and empirical equations have been derived to accurately calculate sound speed from these variables. [*[*] Other factors affecting sound speed are minor. For more information see Dushaw et al.*http://handle.dtic.mil/100.2/ADB199453 APL-UW TR 9407 High-Frequency Ocean Environmental Acoustic Models Handbook*] , pp. I1-I2.A simple empirical equation for the speed of sound in sea water with reasonable accuracy for the world's oceans is due to Mackenzie: [

*cite journal*] :"c"("T", "S", "z") = "a"

author = Mackenzie, Kenneth V.

title = Discussion of sea-water sound-speed determinations

year = 1981

journal = Journal of the Acoustical Society of America

volume = 70

issue = 3

pages = 801-806

doi = 10.1121/1.386919_{1}+ "a"_{2}"T" + "a"_{3}"T"^{2}+ "a"_{4}"T"^{3}+ "a"_{5}("S" - 35) + "a"_{6}"z" + "a"_{7}"z"^{2}+ "a"_{8}"T"("S" - 35) + "a"_{9}"Tz"^{3}where "T", "S", and "z" are temperature in degrees Celsius, salinity in parts per thousand and depth in metres, respectively. The constants "a"_{1}, "a"_{2}, ..., "a"_{9}are::"a"_{1}= 1448.96, "a"_{2}= 4.591, "a"_{3}= -5.304×10^{-2}, "a"_{4}= 2.374×10^{-4}, "a"_{5}= 1.340, "a"_{6}= 1.630×10^{-2}, "a"_{7}= 1.675×10^{-7}, "a"_{8}= -1.025×10^{-2}, "a"_{9}= -7.139×10^{-13}with check value 1550.744 m/s for "T"=25 °C, "S"=35‰, "z"=1000 m. This equation has a standard error of 0.070 m/s for salinities between 25 and 40ppt . See [*http://www.npl.co.uk/acoustics/techguides/soundseawater/ Technical Guides - Speed of Sound in Sea-Water*] for an online calculator.Other equations for sound speed in sea water are accurate over a wide range of conditions, but are far more complicated, e.g., that by V. A. Del Grosso [

*cite journal*] and the Chen-Millero-Li Equation. [

author = Del Grosso, V. A.

title = New equation for speed of sound in natural waters (with comparisons to other equations)

year = 1974

journal = Journal of the Acoustical Society of America

volume = 56

issue = 4

pages = 1084-1091

doi = 10.1121/1.1903388*cite journal*] cite journal

last = Meinen | first = Christopher S.

coauthors = Watts, D. Randolph

title = Further evidence that the sound-speed algorithm of Del Grosso is more accurate than that of Chen and Millero

year = 1997

journal = Journal of the Acoustical Society of America

volume = 102

issue = 4

pages = 2058-2062

doi = 10.1121/1.419655

last = Dushaw |first = Brian D.

coauthors = Worcester, P.F.; Cornuelle, B.D.; and Howe, B.M.

title = On equations for the speed of sound in seawater

year = 1993

journal = Journal of the Acoustical Society of America

volume = 93

issue = 1

pages = 255-275

doi = 10.1121/1.405660]**peed in plasma**The speed of sound in a plasma for the common case that the electrons are hotter than the ions (but not too much hotter) is given by the formula (see here):$c\_s\; =\; (gamma\; ZkT\_e/m\_i)^\{1/2\}\; =\; 9.79\; imes10^5,(gamma\; ZT\_e/mu)^\{1/2\},mbox\{cm/s\}$In contrast to a gas, the pressure and the density are provided by separate species, the pressure by the electrons and the density by the ions. The two are coupled through a fluctuating electric field.

**Gradients**When sound spreads out evenly in all directions, the intensity drops in proportion to the inverse square of the distance. However, in the ocean there is a layer called the 'deep sound channel' or

SOFAR channel which can confine sound waves at a particular depth, allowing them to travel much further. In the SOFAR channel, the speed of sound is lower than that in the layers above and below. Just as light waves will refract towards a region of higher index, sound waves will refract towards a region where their speed is reduced. The result is that sound gets confined in the layer, much the way light can be confined in a sheet of glass oroptical fiber .A similar effect occurs in the atmosphere.

Project Mogul successfully used this effect to detect a nuclear explosion at a considerable distance.**References*** Applied Physics Laboratory - University of Washington, 1994

**ee also***

Second sound

*Sound barrier

*SOFAR channel

*Underwater acoustics **External links*** [

*http://www.sengpielaudio.com/calculator-speedsound.htm Calculation: Speed of sound in air and the temperature*]

* [*http://www.sengpielaudio.com/SpeedOfSoundPressure.pdf Speed of sound - temperature matters, not air pressure*]

* [*http://www.pdas.com/atmos.htm Properties Of The U.S. Standard Atmosphere 1976*]

* [*http://www.mathpages.com/home/kmath109/kmath109.htm The Speed of Sound*] at MathPages

* [*http://www.bustertests.co.uk/answer/how-to-measure-the-speed-of-sound-in-a-laboratory/ How to measure the speed of sound in a laboratory*]

* [*http://twt.mpei.ac.ru/MAS/Worksheets/wspWPT.mcd Speed of sound in water and water steam as function of pressure & temperature*]

* [*http://www.acoustics.salford.ac.uk/schools/index1.htm Teaching resource for 14-16yrs on sound including speed of sound*]

* [*http://www.npl.co.uk/acoustics/techguides/soundpurewater/ Technical Guides - Speed of Sound in Pure Water*]

* [*http://www.npl.co.uk/acoustics/techguides/soundseawater/ Technical Guides - Speed of Sound in Sea-Water*]

* [*http://www.newbyte.co.il/calc.html NewByte standard atmosphere calculator and speed converter*]

* [*http://space.newscientist.com/article/mg19826504.200-did-sound-once-travel-at-light-speed.html?feedId=online-news_rss20 Did sound once travel at light speed?*] - If the speed of sound was greater just after the big bang, it could solve a longstanding mystery over the universe's background temperature ("New Scientist", 9 April 2008)

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2010.*