(i) Effect of pressure
(ii ) Effect of temperature
(iii)Effect of density
(iv) Effect of humidity
(v ) Effect of wind

**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 v_{o} and v_{t} be
the velocity of sound at O^{o} C and to C respectively. Then, from the
above equation,

v_{o}
= root [ γ R/m ? 273 ]

∴ v_{t} = v_{0}
= root[1+(t/273)]^{1/2}

Using
binomial expansion and neglecting higher powers we get

v_{t}
= v_{0} = root[1+(t/546)]

Since
v_{0} = 331 m s^{-1} at 0^{0} C

V_{t}
= 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

v_{1}
= γ_{1} P / ρ_{1} and v_{2}
= γ_{2} P / ρ_{2}

For
gases having same value of γ,

v_{1
}/ v_{2} = root[ρ_{2}/ ρ_{1} ]

*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

Helium 965

Hydrogen 1284

Liquids Water 0o C 1402

Water at 20o C 1482

Sea water 1522

Solids Aluminum 6420

Steel 5921

Granite 6000

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