JEE Main & Advanced Physics Wave Mechanics Factors Affecting Velocity of Sound in Gaseous Medium

(1) Effect of pressure at constant temperature : Velocity of sound is independent of the pressure of gas, because as pressure increases, density also increases hence \[\frac{P}{\rho }\] ratio remains constant. So from \[\upsilon =\sqrt{\frac{\gamma \,P}{\rho }},\]

(2) Effect of temperature : With rise in temperature velocity of sound increases.

\[v\,=\,\sqrt{\frac{\gamma RT}{M}}\]\[\Rightarrow \]\[v\,\propto \sqrt{T}\]\[\Rightarrow \]\[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{{{T}_{1}}}{{{T}_{2}}}}=\sqrt{\frac{(273+{{t}_{1}}{}^\circ C)}{(273+{{t}_{2}}{}^\circ C)}}\]

When the temperature change is small then \[{{v}_{t}}={{v}_{0}}+0.61\,t\]

where \[{{\upsilon }_{t}}=\] Velocity of sound at \[{{t}^{o}}C\]

\[{{\upsilon }_{0}}=\] Velocity of sound at \[{{0}^{o}}C=332\,\,m/\sec \]

\[t=\] Small temperature change

If \[t={{1}^{o}}C\] then \[{{v}_{t}}=({{v}_{0}}+0.61)\,m/sec\]. Hence for \[{{1}^{o}}C\] rise, speed of sound in air increases by 0.61 m/sec.

(3) Effect of density : v = \[\sqrt{\frac{\gamma \,P}{\rho }}\]Þ v \[\propto \frac{1}{\sqrt{\rho }}\] 

(4) Effect of humidity : With increase in humidity, density of air decreases. So with rise in humidity velocity of sound increases.

Sound travels faster in humid air (rainy season) than in dry air (summer) at the same temperature because

\[{{\rho }_{moist\,air}}<{{\rho }_{dry\,air}}\,\,\,\Rightarrow \,\,{{v}_{moist\,air}}>\,{{v}_{dry\,air}}\]

(5) Effect of wind velocity : Because wind drifts the medium (air) along its direction of motion therefore the velocity of sound in a particular direction is the algebraic sum of the velocity of sound and the component of wind velocity in that direction. Resultant velocity of sound towards observer \[\upsilon '=\upsilon +w\cos \theta \].

(6) Sound of any frequency or wavelength travels through a given medium with the same velocity.

For a given medium velocity remains constant. All other factors like phase, loudness pitch, quality etc. have practically no effect on sound velocity.