# Speed of sound

The speed of sound is the speed at which sound vibrations or sound waves travel. Sound can only travel in a medium (solid, liquid or gaseous) and the speed
v
{\displaystyle v}
depends on the compression modulus
κ
{\displaystyle \kappa }
and the density
ρ
{\displaystyle \rho }
of the medium, according to the following formula:
v
κ
ρ
{\displaystyle v{\sqrt {\frac {\kappa }{\rho }}}}
The density and the compression modulus can depend on, among other things, the temperature and, for example, the moisture content. For air at room temperature (20°C), the speed of sound is approximately 343 meters per second or 1234.8 km/h. In dry air (with relatively little water vapour) with a temperature of 0 °C, this is 331 m/s or 1191.6 km/h. In liquids and solids, the speed of sound is usually higher. In water, for example, sound travels at a speed of approximately 1510 m/s; in wood this is approximately 3300 m/s; in steel approximately 5800 m/s. With the hardest metals, the speed of sound can be as high as 12,000 m/s.
When an aircraft flies faster than the speed of sound in the air at that altitude, it produces a shock wave called 'breaking the sound barrier'. The Mach number is derived from this.

## Speed of sound in air

A formula that connects the speed of sound c in an ideal gas (in aerodynamics the letter a is often used) with the temperature is:
c
γ
R
T
m
{\displaystyle c{\sqrt {\gamma {\frac {RT}{M}}}}}
;in it is
γ
C
p
/
C
v
{\displaystyle \gamma {C_{p}}/{C_{v}}}
the specific heat ratio (for air 1.41), R the general gas constant (8.3145 J/(mol K)), T the absolute temperature in Kelvin and M the molar mass of the gas in kg/mol.
The compressibility and density of an air are well approximated by the general gas law.
The specific heat ratio is a correction, because due to the rapid adiabatic compression, the temperature increases the moment the air is compressed by the sound wave and after passing the temperature decreases again. The higher temperature reduces the compressibility and the effect is an increase in the speed of sound.
For air, the above formula can be approximated by:
c
≈
20
273
+
θ
≈
(
331
,
5
+
0
,
6
θ
)
(
m
/
s
)
{\displaystyle c\approx 20{\sqrt {273+\vartheta }}\approx (331{,}5+0{,}6\ \vartheta )\ \mathrm {(m/s)} }
,of
θ
{\displaystyle \vartheta }
the temperature in degrees Celsius. The speed increases with temperature, at 20 °C the speed of sound is about 12 m/s greater than at 0 °C. The speed of sound is almost independent of the frequency of the sound and also of the air pressure, but nevertheless the deviations are measurable and also audible. The speed of sound relative to the ground can of course be