Factors affecting velocity of sound in gases
(i) Effect of pressure
If the temperature of the gas remains constant, then by Boyle?s law PV = constant
i.e P . m / ρ = constant
P / ρ is a constant, when mass (m) of a gas is constant. If the pressure changes from P to P ′ then the corresponding density also will change from ρ to ρ ′ such that P ρ is a constant.
In Laplace?s formula root(γP / p) is also a constant. Therefore the velocity of sound in a gas is independent of the change in pressure provided the temperature remains constant.
(ii ) Effect of temperature
For a gas, PV = RT
P.m/p = RT
P. /p = RT/ m
where m is the mass of the gas, T is the absolute temperature and R is the gas constant.
Therefore v = root(γRT/m)
It is clear that the velocity of sound in a gas is directly proportional to the square root of its absolute temperature. Let vo and vt be the velocity of sound at Oo C and to C respectively. Then, from the above equation,
vo = root [ γ R/m ? 273 ]
∴ vt = v0 = root[1+(t/273)]1/2
Using binomial expansion and neglecting higher powers we get
vt = v0 = root[1+(t/546)]
Since v0 = 331 m s-1 at 00 C
Vt = 331 + 0.61 m s-1
Thus the velocity of sound in air increases by 0.61 m s?1 per degree centigrade rise in temperature.
(iii)Effect of density
Consider two different gases at the same temperature and pressure with different densities. The velocity of sound in two gases are given by
v1 = γ1 P / ρ1 and v2 = γ2 P / ρ2
For gases having same value of γ,
v1 / v2 = root[ρ2/ ρ1 ]
The velocity of sound in a gas is inversely proportional to the square root of the density of the gas.
(iv) Effect of humidity
When the humidity of air increases, the amount of water vapour present in it also increases and hence its density decreases, because the density of water vapour is less than that of dry air. Since velocity of sound is inversely proportional to the square root of density, the sound travels faster in moist air than in dry air. Due to this reason it can be observed that on a rainy day sound travels faster.
(v ) Effect of wind
The velocity of sound in air is affected by wind. If the wind blows with the velocity w along the direction of sound, then the velocity of sound increases to v + w. If the wind blows in the opposite direction to the direction of sound, then the velocity of sound decreases to v ? w. If the wind blows at an angle θ with the direction of sound, the effective velocity of sound will be (v + w cos θ).
Note: In a medium, sound waves of different frequencies or wavelengths travel with the same velocity. Hence there is no effect of frequency on the velocity of sound.
Velocity of sound in various media
Medium Velocity (ms?1)
Gases Air 0o C 331
Air 20o C 343
Liquids Water 0o C 1402
Water at 20o C 1482
Sea water 1522
Solids Aluminum 6420
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