Speed of sound

     From Wikipedia, the free encyclopedia.

The speed of sound c (mostly in air) 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 humidity affects very little the speed of sound nor does it the static sound pressure (air pressure), but most important is the temperature. Sound travels slower with an increased altitude (elevation if you're on solid earth). This is primarily a function of temperature and humidity changes and not the sound pressure. An approximate speed (in metres/second) can be calculated from:

where (theta) is the temperature in degrees Celsius.

A more accurate expression is

where R is the gas constant (287.05 J/kgK for air), κ (kappa) is the adiabatic index (1.402 for air), and T is the absolute temperature in kelvin. In the standard atmosphere, T₀ is 288.15 K (= 15°C, 59°F), giving a value of 340 m/s (= 1225 km/h, 761 mph, 661 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 condititions may vary)

Altitude	Temperature	m/s	km/h	mph	knots
Sea level	15°C (59°F)	340	1225	761	661
(Cruising altitude of commercial jets, and Bell_X-1>first supersonic flight)	-57°C (-70°F)	295	1062	660	574
X-43A)	-48°C (-53°F)	301	1084	674	585

In fluids, using the theory of compressible flow, the speed of sound can be calculated using

This is correct for adiabatic flow; Newton famously used isothermal calculations and omitted the κ from the numerator.

In an ideal gas the speed of sound is really only depending on the temperature and not of the air pressure. Air is nearly an ideal gas. Notice: Therefore the speed of sound is not depending on the air pressure.

In solids the speed of sound is given by:

where E is Young's modulus and ρ (rho) is density. Thus in steel the speed of sound is approximately 5100 m/s.
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. == Table - Speed of sound in air c, density of air ρ,
acoustic impedance Z vs. temperature °C ==

Impact of temperature
°C	c	ρ	Z
- 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

See also Mach number.

External Weblinks

• Calculation: Speed of sound in air and the temperature
• The speed of sound, the temperature, and ... not the air pressure
• Properties Of The U.S. Standard Atmosphere 1976