Velocity of Sound in a Gas

To derive a relation for the velocity of sound in a gaseous medium, newton assumed that compression and rarefaction caused by the sound waves during their passage through the gas take place under isothermal condition. This means that the changes in volume and pressure take place at constant temperature.

Under such conditions, Newton agreed that the velocity of sound wave in a gas is given by

v = √(P/ρ)

For air, at standard temperature and pressure P = 1.01 × 105 Nm–2 and ρ = 1.29 kg m–3. On substituting these values,

v = 280 ms–1

Clouds collide producing thunder and lightening, you hear sound of thunder after the lightening. This is because the velocity of light is very much greater than the velocity of sound in air.

By measuring the time interval between observing the lightening and hearing the sound, the velocity of sound in air can be determined. Using an improved technique, the velocity of sound in air has been determined as 333 ms–1 at 0°C.

The percent error in the value predicted by Newton’s formula and that determined experimentally is 16%. This error is too high to be regarded as an experimental error. There is something wrong with Newton’s assumption that during the passage of sound, the compression and the rarefaction of air take place isothermally.