Question

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

Answer 1

Hint: 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.