## Effect of various factors on the speed of sound

Effect of various factors on the speed of sound

### (1)Effect of pressure

From Laplace’s formula for the speed of sound in a gas, v =√ (ϒP/ρ), it appears that the speed of sound (v) must change with change in pressure. But actually it is not like that Consider 1 gm-molecule of gas whose pressure and volume are P and V respectively. If T be the absolute temperature of the gas, then according to the gas equation: PV = RT, where R is the universal gas constant. If molecular weight of the gas be M and density is ρ, then V = M/ρ, and we get:

P (M/ρ) = RT or P/ρ = RT/M= constant.

Here if T is constant i.e., at the constant temperature, if P changes then ρ also changes in such a way that the ratio P/ρ remains constant. Hence, in the Laplace’s formula v =√ (ϒP/ρ), the value of P/ρ does not change when P changes. From this it is clear that if the temperature of the gas remains constant, then there is no effect of the pressure change on the speed of sound.

### (2)Effect of temperature:

(A) As we have seen above, the value of P/ ρ for a gas depends upon the temperature of the gas. If we supply heat to gas, there are two possibilities.

(i) If the gas is free to expand, then on being heated its volume will increase while pressure will remains constant i.e., its density ρ would decreases and pressure will remain constant i.e., the value of ratio P/ρ will increase.

(ii) If the gas is closed in a vessel, then on being heated its pressure will increase while the density will not change i.e., again the value of the ratio P/ρ will increase.

Thus in both situations, the speed of sound will increase with increase in the temperature of the gas.

(B) We have seen above that for a gas P/ρ = RT/M, where M is the molecular weight of the gas and T is the temperature. Hence the speed of sound in the gas is :

v =√ (ϒ P/ρ) =√ (ϒRT/M) …..(1)

Thus it is clear from above equation that the speed of sound I a gas is directly proportional to the square-root of its absolute temperature.

(C)Now, if v_{0} be the speed of 0°C and vt the speed at t°C, then from the above equation, we get

V_{0} =√ (ϒR/ρ) √(273) ….(2)

And v_{t} =√ (ϒR/ρ) √(273+ t) …..(3)

Dividing equation (3) by (2) and assuming the speed of sound in air at 0°C as 331 m/s, we get:

V_{t} =331[1+t/(2 × 273)]= (331 + 0.61 t) m/s

Thus, the velocity of sound in air increases roughly by 0.61 m/s per degree centigrade rise in temperature.

### (3) Effect of density:

Consider two gasses having same value of ϒ(both monatomic or both diatomic or both tri-atomic) and at the same pressure P. Let their densities be ρ_{1} and ρ_{2} respectively. Then velocities of sound in the two gases are given by:

v_{1} =√ (ϒ P_{1}/ρ) and v2 =√ (ϒ P_{2}/ρ)

Or v_{1}/v_{2} = =√ (ρ_{1}/ρ_{2})

This shows that at constant pressure, velocity of sound in a gas is inversely proportional to the square root of its density. The velocity of sound in hydrogen is greater than that in oxygen because hydrogen is a lighter gas.

### (4)Effect of humidity:

When moisture is present in air, the density of air get decreased It is because the density of water vapours is less than that of dry air. Because, velocity of sound is inversely proportional to the square root of density, hence sound travels faster in moist air than in the dry air. Higher is the humidity in the air, higher will be velocity of sound. This is the reason that on a rainy day sound travels faster than on a dry day.

### (5)Effect of wind:

The velocity of sound is also affected by the wind velocity. Suppose S is a source of sound and O is an observer as shown in following figure. The sound travels along SO with a velocity v. If the wind blow with a velocity u in the direction say SQ making an angle θ with SO, then the component of wind velocity along SO is u cos θ. This component is added to the velocity v of sound and the sound travels in the direction SO with the resultant velocity. V= v + u cos θ.

If the wind blows in the direction of the transmission of sound i.e., θ = 0, then cos 0° =1 or V = v + u

If the wind blow in the direction opposite to that of transmission of sound i.e., if θ = 180°, then cos 180°= -1. Or V = v –u

Thus, sound will travel faster, if θ is acute and slower, if θ is obtue. The wind will have no effect on the velocity of sound, if θ = 90°

### (6)Effect of frequency:

There is no effect of frequency on the speed of sound. Sound waves of different frequencies travel with the same speed in air although their wavelengths in air are different. In case, the speed of sound through air depended on the frequency of sound, then we could not have enjoyed orchestra.

### (7) Effect of amplitude:

If amplitude of sound waves is very large, the compression and rarefaction may result in large temperature variations and this may affect the velocity of sound.