Speed of sound
From Academic Kids

 "Speed of Sound" is also a single by Coldplay.
The speed of sound c (from Latin celeritas, "velocity") varies depending on the medium through which the sound waves pass. It is usually quoted in describing properties of substances (e.g. see the article on sodium).
More commonly the term refers to the speed of sound in air. The speed varies depending on atmospheric conditions; the most important factor is the temperature. The humidity has very little effect on the speed of sound, while the static sound pressure (air pressure) has none. Sound travels slower with an increased altitude (elevation if you are on solid earth), primarily as a result of temperature and humidity changes. An approximate speed (in metres per second) can be calculated from:
 <math>
c_{\mathrm{air}} = (331{.}5 + 0{.}6 \cdot \vartheta) \ \mathrm{m/s} <math>
where <math>\vartheta<math> (theta) is the temperature in degrees Celsius.
A more accurate expression is
 <math>
c = \sqrt {\kappa \cdot R\cdot T} <math>
where
 R (287.05 J/(kg·K) for air) is the universal gas constant (In this case, the gas constant R, which normally has units of J/(mol·K), is divided by the molar mass of air, as is common practice in aerodynamics)
 κ (kappa) is the adiabatic index (1.402 for air), sometimes noted γ
 T is the absolute temperature in kelvins.
In the standard atmosphere:
T_{0} is 273.15 K (= 0 °C = 32 °F), giving a value of 331.5 m/s (= 1087.6 ft/s = 1193 km/h = 741.5 mph = 643.9 knots).
T_{20} is 293.15 K (= 20 °C = 68 °F), giving a value of 343.4 m/s (= 1126.6 ft/s = 1236 km/h = 768.2 mph = 667.1 knots).
T_{25} is 298.15 K (= 25 °C = 77 °F), giving a value of 346.3 m/s (= 1136.2 ft/s = 1246 km/h = 774.7 mph = 672.7 knots).
In fact, assuming an ideal gas, the speed of sound c depends on temperature only, not on the pressure. 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.
Altitude  Temperature  m/s  km/h  mph  knots 
Sea level  15 °C (59 °F)  340  1225  761  661 
11,000 m–20,000 m (Cruising altitude of commercial jets, and first supersonic flight)  57 °C (70 °F)  295  1062  660  573 
29,000 m (Flight of X43A)  48 °C (53 °F)  301  1083  673  585 
In a NonDispersive Medium – Sound speed is independent of frequency, therefore the speed of energy transport and sound propagation are the same. Air is a nondispersive medium.
In a Dispersive Medium – Sound speed is a function of frequency. The spatial and temporal distribution of a propagating disturbance will continually change. Each frequency component
propagates at each its own phase speed, while the energy of the disturbance propagates at the
group velocity. Water is an example of a dispersive medium.
In general, the speed of sound c is given by
 <math>
c = \sqrt{\frac{C}{\rho}} <math> where
 C is a coefficient of stiffness
 <math>\rho<math> is the density
Thus the speed of sound increases with the stiffness of the material, and decreases with the density.
In a fluid the only nonzero stiffness is to volumetric deformation (a fluid does not sustain shear forces).
Hence the speed of sound in a fluid is given by
 <math>
c = \sqrt {\frac{K}{\rho}} <math> where
 K is the adiabatic bulk modulus
For a gas, K is approximately given by
 <math>
K=\kappa \cdot p <math>
where
 κ is the adiabatic index, sometimes called γ.
 p is the pressure.
Thus, for a gas the speed of sound can be calculated using:
 <math>
c = \sqrt {{\kappa \cdot p}\over\rho} <math> which using the ideal gas law is identical to:
<math> c = \sqrt {\kappa \cdot R\cdot T} <math>
(Newton famously used isothermal calculations and omitted the κ from the numerator.)
In a solid, there is a nonzero 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.
In a solid rod (with thickness much smaller than the wavelength) the speed of sound is given by:
 <math>
c = \sqrt{\frac{E}{\rho}} <math>
where
 E is Young's modulus
 <math>\rho<math> (rho) is density
Thus in steel the speed of sound is approximately 5100 m/s.
In a solid with lateral dimensions much larger than the wavelength, the sound velocity is higher. It is found be replacing Young's modulus with the plane wave modulus, which can be expressed in terms of the Young's modulus and Poisson's ratio as:
 <math>
M = E \frac{1\nu}{1\nu2\nu^2} <math>
For air, see density of air.
The speed of sound in water is of interest to those mapping the ocean floor. In saltwater, sound travels at about 1500 m/s and in freshwater 1435 m/s. These speeds vary due to pressure, depth, temperature, salinity and other factors.
For general equations of state, if classical mechanics is used, the speed of sound <math>c<math> is given by
 <math>
c^2=\frac{\partial p}{\partial\rho}<math> where differentiation is taken with respect to adiabatic change.
If relativistic effects are important, the speed of sound <math>S<math> is given by:
 <math>
S^2=c^2 \left. \frac{\partial p}{\partial e} \right_{\rm adiabatic} <math>
(Note that <math> e= \rho (c^2+e^C) \,<math> is the relativisic internal energy density; see relativistic Euler equations).
This formula differs from the classical case in that <math>\rho<math> has been replaced by <math>e/c^2 \,<math>.
Table  Speed of sound in air c, density of air ρ and acoustic impedance Z vs. temperature °C
Impact of temperature  
<math>\vartheta<math> in °C  c in m/s  ρ in kg/m³  Z in N·s/m³ 
10  325.4  1.341  436.5 
5  328.5  1.316  432.4 
0  331.5  1.293  428.3 
+5  334.5  1.269  424.5 
+10  337.5  1.247  420.7 
+15  340.5  1.225  417.0 
+20  343.4  1.204  413.5 
+25  346.3  1.184  410.0 
+30  349.2  1.164  406.6 
Mach number is the ratio of the object's speed to the speed of sound in air (medium).
External links
 Calculation: Speed of sound in air and the temperature (http://www.sengpielaudio.com/calculatorspeedsound.htm)
 The speed of sound, the temperature, and ... not the air pressure (http://www.sengpielaudio.com/SpeedOfSoundPressure.pdf)
 Properties Of The U.S. Standard Atmosphere 1976 (http://www.pdas.com/atmos.htm)ca:velocitat del so
de:Schallgeschwindigkeit es:Velocidad del sonido fr:Vitesse du son he:מהירות הקול ja:音速 nl:Geluidssnelheid pt:Velocidade do som sl:hitrost zvoka sv:Ljudhastighet it:Velocità del suono zh:音速