Question

Helium is a monoatomic gas that has a density of $0.179kg/m^3$ at a pressure of 76 cm mercury and a temperature of $0^{\circ }C$. Find the speed of compressional waves (sound) in helium at this temperature and pressure. (in m/s)

Answer 1

We have , speed of sound in a gas ,

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

where $P=$ pressure of gas ,

$\gamma =$ ratio of specific heats ,

$\rho =$ density of gas ,

given $P=76cmHg=1.01\times {10}^{5}N/m^2,\rho =0.179kg/m^3,\gamma =1.67$ (as He is a monoatomic gas) ,

therefore speed of sound in He gas ,

$v=\sqrt{1.67\times 1.01\times {10}^5/0.179}=970.8m/s$