Question

The velocity of sound in gas is independent of _______. Fill in the blank.

• A. pressure
• B. density
• C. temperature
• D. humidity

Answer 1

Answer: (A)

The velocity of sound $v$ in a gas is given by Laplace formula ,

$v=\sqrt{\gamma P/\rho }$ ,

where , $P=$ pressure of gas ,

$\rho =$ density of gas ,

$\gamma =$ ratio of specific heats at constant pressure and volume ,

for 1 mole of gas , $PV=RT$ ,

where volume of gas , $V=M/\rho$ ,($M=$ mass of one mole of gas or molecular mass) ,

so we have , $P\left(M/\rho \right)=RT$ ,

or $P/\rho =RT/M=$constant , if $T$(temperature of the gas ) is constant ,

therefore at constant temperature , ratio $P/\rho$ , remains constant hence velocity remains constant therefore we can say that pressure change has no effect on velocity of sound in a gas .