**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.**

ANSWER

**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 v_{0} and v are the respective speeds of sound in air/gas at temperatures T_{0} and T, respectively, then from equation (A)

Divide the second equation by the first,

Now if T =(t + 273)K and T_{0} = (0+ 273) K, then

Hence for each degree rise in temperature, the speed of sound is increased by 0.61m/s.

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