Question

Velocity of sound in a gas proportional to

• A. square root of isothermal elasticity
• B. isothermal elasticity
• C. square root of adiabatic elasticity
• D. adiabatic elasticity

Answer 1

Answer: (C)

square root of adiabatic elasticity

According to the Laplace's formula for velocity of sound in gases,

$v=\sqrt{\frac{E}{\rho }}$

where, $E=\gamma p$ is the adiabatic elasticity and $\rho$ is the density of gas.

This is because the compression and rarefaction occurs rapidly one after another without exchanging the thermal energy with surrounding hence, this the process becomes adiabatic and not the isothermal. Hence, velocity of sound in a gas proportional to square root of adiabatic elasticity