Question

The velocity of sound at ${15}^{\circ }C$ and 380 mm pressure is 340 m/s. If the temperature remains constant and pressure is doubled, the velocity of sound will be

• A. 340 m/s
• B. 170 m/s
• C. 680 m/s
• D. None of these

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 .

As in the given question , temperature is constant therefore velocity of sound will also remain constant i.e. 340m/s .