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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/second) can be calculated from: (The proposal to take the letter v for speed of sound instead of c for speed of light is not generally accepted.)
where (theta) is the temperature in degrees Celsius.
A more accurate expression is
where R (287.05 J/kgK for air) is the universal gas constant R divided by the molar mass of air, κ (kappa) is the adiabatic index (1.402 for air), sometimes called γ, and T is the absolute temperature in kelvins. In the standard atmosphere:
T0 is 273.15 K (= 0 °C = 32 °F), giving a value of 331.5 m/s (= 1193 km/h = 741.5 mph = 643.9 knots).
T20 is 293.15 K (= 20 °C = 68 °F), giving a value of 343.4 m/s (= 1236 km/h = 768.2 mph = 667.1 knots).
T25 is 298.15 K (= 25 °C = 77 °F), giving a value of 346.3 m/s (= 1246 km/h = 774.7 mph = 672.7 knots).
In fact, assuming a perfect gas the speed of sound depends on temperature only, not on the pressure. Air is almost a perfect 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 |
| 11000m-20000m (Cruising altitude of commercial jets, and first supersonic flight) | -57 °C (-70 °F) | 295 | 1062 | 660 | 573 |
| 29000m (Flight of X-43A) | -48 °C (-53 °F) | 301 | 1083 | 673 | 585 |
In a Non-Dispersive Medium – Sound speed is independent of frequency, therefore the speed of energy transport and sound propagation are the same. Air is a non-dispersive 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 is given by
where C is a coefficient of stiffness and is the densityFor other meanings of density, see density (disambiguation Density (symbol: rho Greek: rho) is a measure of mass per unit of volume. The higher an object's density, the higher its mass per volume. The average density of an object equals its total mass div.
Thus the speed of sound increases with the stiffness of the material, and decreases with the density.
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
where K is the adiabatic bulk modulusThe bulk K modulus of a fluid or solid is the inverse of the compressibility: where p is pressure and V is volume. The bulk modulus thus measures the response in pressure due to a change in relative volume. For a solid pressure should be replaced by the m For a gas, K is approximately given by
where
κ is the adiabatic index, sometimes called γ.
p is the pressurePressure (symbol: p is a measure of force per unit area. where p is the pressure F is the force A is the area Often F is taken to be the of the magnitude of the mean vector force normal to the surface of area A upon which it exerts; the "surface" not nece.
Thus, for a gas the speed of sound can be calculated using:
which using the ideal gas law is identical to:
(Newton famously used isothermal calculations and omitted the κ from the numerator.)
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.
In a solid rod (with thickness much smaller than the wavelength) the speed of sound is given by:
where
E is Young's modulusIn solid mechanics, Young's modulus or modulus of elasticity (and also elastic modulus is a measure of the stiffness of a given material. It is defined as the limit for small strains of the rate of change of stress with strain. This can be experimentally
ρ (rho) is densityFor other meanings of density, see density (disambiguation Density (symbol: rho Greek: rho) is a measure of mass per unit of volume. The higher an object's density, the higher its mass per volume. The average density of an object equals its total mass div
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:
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 is given by
where differentiation is taken with respect to adiabatic change. If relativistic effects are important, the speed of sound is given by:
(note that is the relativisic internal energy density; see relativistic Euler equations). This formula differs from the classical case in that has been replaced by .
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