Question

If the speed of light in a medium at a given temperature is 348m/s at a pressure of 2atm. Now the pressure is increased to 5 atm, temperature remaining constant. Now the speed of sound in the same medium will be :

• A. less than 348m/s
• B. greater than 348m/s
• C. equal to 348m/s
• D. none

Answer 1

Answer: (C)

equal to 348m/s

In solid and liquid media , speed of sound doesn't depend upon pressure if temperature is constant .

Now 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 i.e . the speed of sound in medium will remain $348m/s$ .