Question 7: How the speed of sound in air varies with temperature? Show that for each degree rise in temperature speed of sound increases by 0.61 m/s.
Speed of sound and temperature
Consider one mole of a gas having volume ‘V’, pressure ‘P’ and temperature ‘T’. Applying gas law, (PV = nRT), we have, (since n = 1).
Substitute the value of ρ from equation (2) in the equation for speed of sound,
This shows the speed of sound is directly proportional to the square root of the temperature.
Speed of sound per degree rise in temperature
If v0 and v are the respective speeds of sound in air/gas at temperatures T0 and T, respectively, then from equation (A)
Divide the second equation by the first,
Now if T =(t + 273)K and T0 = (0+ 273) K, then
Hence for each degree rise in temperature, the speed of sound is increased by 0.61m/s.