Sound waves
Sound waves are longitudinal waves propagated through a
material by the transfer of kinetic energy from one molecule to another
(a) in solids
and liquids by intermolecular forces and collisions,
(b) in gases by intermolecular
collisions alone.
Hence the velocity of sound is greater in solids and liquids than in
gases (the intermolecular forces in a gas are very small or zero).
The velocity of sound
in a gas will thus be slightly less than the root mean square velocity of the gas molecules
themselves. It will increase with increasing temperature since this will give a larger molecular
velocity.
The table below gives the velocity of sound in a number of materials.
Material 
Velocity of sound (ms^{1}) 

Material 
Velocity of sound (ms^{1}) 
Air (273 K) 
330 

Aluminium 
5100 
Water (298 K) 
1430 

Copper 
3650 
Steel 
5060 

Iron 
5130 
Vulcanised rubber 
54 

Glass 
4000  5500 
Granite (293 K) 
6000 

Pine 
3313 
Hydrogen (273 K) 
1286 

Oak 
3837 
Lead 
1230 

Elm 
4108 
The velocity of sound v in a solid in the form of a rod or wire may be found from the
formula:
Velocity of sound (v) = [E/ρ]^{1/2}
where E is the
Young modulus for the material and ρ is its density
For
an ideal gas the formula becomes:
Velocity of sound (v) in a gas = [γP/ρ]^{1/2}
where P is the gas pressure and γ the ratio of the principal specific heat capacities of the gas.
Substituting for P from PV = RT we have:
Velocity of sound (v) in a gas = [γRT/M]^{1/2}
where M (=
rV)
is the molar mass of the gas.
This last equation shows that the velocity of sound in an
ideal gas is:
(a) independent of the gas pressure,
(b) directly proportional to the
square root of the absolute temperature,
directly proportional to the square root of
g(d) inversely proportional to the square root of the molar mass
of the gas.
It is for this reason that the velocity of sound at high altitude is low since the
air there is cooler. The speed of an aircraft relative to the speed of sound (its Mach number)
is therefore greater when it flies at high altitude even though its actual speed may be the
same as that before it began to climb. The change in the velocity of sound with temperature
also explains why an instrument such as a flute becomes sharp when taken into a warm
concert hall, the frequency change being greater than any effects due to the expansion of
the instrument.
Humidity and the speed of sound
The presence of
water vapour in the atmosphere, known as humidity, causes a slight increase in the velocity
of sound as the humidity rises.
The speed of sound in a gas in inversely proportional to
the square root of the molecular weight of the gas through which the sound is passing the
speed of sound will be greater in moist air. This is because the molecular weight of water is
less than that of dry air.
At 20
^{o}C 100 kPa and 0% humidity the speed of
sound is 343.4 m/s.
At 20
^{o}C 100 kPa and 50% humidity the speed of sound is
344 m/s.
At 20
^{o}C 100 kPa and 90% humidity the speed of sound is 344.5
m/s.
At 20
^{o}C 100 kPa and 100% humidity the speed of sound is 344.6
m/s.
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