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Factors Affecting Speed of Sound

Factors Affecting Speed of Sound :- Several factors affect the speed of sound in a medium like air :-

(1) Effect of temperature

For a gas γ & M_W are constant and hence from $\displaystyle {{v}_{sound}}=\sqrt{\frac{\gamma RT}{{{M}_{w}}}}$ , we get

$\displaystyle v\propto \sqrt{T}$

$\displaystyle \Rightarrow \frac{{{v}_{t}}}{{{v}_{o}}}=\sqrt{\frac{T}{{{T}_{0}}}}=\sqrt{\frac{t{}^\circ C+273}{273}}$

Here v_t is velocity of sound at t °C and v_o is velocity of sound at 0 °C.

$\displaystyle \Rightarrow {{v}_{t}}={{v}_{o}}{{\left[ 1+\frac{t{}^\circ C}{273} \right]}^{{}^{1}\!\!\diagup\!\!{}_{2}\;}}$

By applying Binomial theorem,

(i) For any gas medium $\displaystyle {{v}_{t}}={{v}_{o}}\left[ 1+\frac{t{}^\circ C}{546} \right]$

(ii) For air $\displaystyle {{v}_{t}}={{v}_{o}}+0.61\times \left( t{}^\circ C \right)\text{ }m/s$

(As v_o = 332 m/s)

(2) Effect of Relative Humidity

Moist air is less dense than dry air so from the expression $\displaystyle {{v}_{sound}}=\sqrt{\frac{\gamma P}{\rho }}$ , we conclude that with rise in humidity velocity of sound increases. This is why sound travels faster in humid air (rainy season) than in dry air (summer) at same temperature. Due to this in rainy season the sound of factories siren and whistle of train can be heard more than summer.

(3) Effect of Pressure

Looking at the expression $\displaystyle {{v}_{sound}}=\sqrt{\frac{B}{\rho }}=\sqrt{\frac{\gamma P}{\rho }}=\sqrt{\frac{\gamma RT}{{{M}_{w}}}}$ , we conclude that, as long as temperature remains constant, there is no effect of change of pressure on speed of sound. This is because as pressure changes, density also changes proportionately.

(4) Effect of Wind

Wind can affect the speed of sound, particularly when it is blowing in the same direction as the sound waves. In such cases, it can increase the speed of sound relative to an observer on the ground, and decrease it when blowing in the opposite direction.

(5) 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 wavelength in air are different. That is why we are able to enjoy orchestra producing sound waves of different frequencies.

Factors Affecting Speed of Sound

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