Question

The difference in the speeds of sound in air at $-5^{o}C$, 60 cm pressure of mercury and ${30}^{0}C$, 75 cm pressure of mercury is :
(velocity of sound in air at $0^{o}C$ is 332 m/s)

• A. 15.25 m/s
• B. 21.35 m/s
• C. 18.3 m/s
• D. 3.05 m/s

Answer 1

The correct option is B 21.35 m/s

The velocity of sound in air (or in other gases) can be expressed as
$c=\sqrt{\frac{\gamma p}{\rho }}$
$\rho =\frac{p}{RT}$
$\therefore c=\sqrt{\gamma RT}$
where
c = sound velocity (m/s, ft/s)
k = ratio of specific heat (adiabatic index, isentropic expansion factor)
p = pressure (Pa, psi)
R = 287.053072 (J/kg K) = 1,716 (ft lb/slug oR) = gas constant specific for air
T = absolute temperature (K, R)
From the above equation, we can see that the speed is independent of pressure.
So, substituting the value of Temperature in the above equation for -5 and 30,we get the difference as 21.35 m/s