Question

Write any two factors that influence the speed of sound through air.

Answer 1

Sound is a longitudinal wave which need a medium for its propagation, speed of sound in fluid is given as v = $\sqrt {B/\rho }$ where $B = {\text{ }}bulk{\text{ }}modulus{\text{ }}of{\text{ }}fluid$, its value depend on the process and $\rho = {\text{ }}density{\text{ }}of{\text{ }}fluid$.

Complete step by step solution:
From the equation v = $\sqrt {\gamma RT/M}$ and v =$\sqrt {\gamma P/\rho }$ we can speed of sound depend on

1. Temperature of air as v \propto $$$$\sqrt T that means on increasing the temperature speed of sound also increases and on decreasing the temperature speed of sound also decreases.

2. Density of air as v \propto $$$$\sqrt {1/\rho } which means on increasing the density of air speed of sound decreases and on decreasing the density of air speed of sound increases.

Additional Information: Sound travel very fast in air so it is considered as adiabatic process and the value of B is taken $\gamma P$ and hence speed of sound in air is taken as v = $\sqrt {\gamma P/\rho }$ and from gas equation $\rho = {\text{ }}PM/RT$ so the speed of sound can be written as $\sqrt {\gamma RT/M}$

Note: From the formula for the speed of sound in a gas v =$\sqrt {\gamma P/\rho }$, it appears that v \propto $$$$\sqrt P , but actually it is not so, because $\dfrac{P}{\rho } = {\text{ }}RT/M{\text{ }} = constant$ at constant temperature.