Derive an expression for frequency, f, of sound as heard by stationary observer when the source of sound of frequency, f, approaches with uniform speed, us

Suppose c is the speed of sound in air, u_s is the speed of source, S, of sound, f is the frequency of source

If the source S were stationery, the f-wave sent out in 1s towards observer would cover a distance, V, and wavelength, λ = c/f

If the source is moving towards a stationary observer, O.

Where u_s is the speed of sound towards O. The sent wave occupy a shorter distance (c-u_s) because S has moved a distance u_s, towards O in 1s. So the wave length λ’ of waves λ’ = (c-u_s)/f.

Apparent frequency, f’;

Since (c-u_s) is less than c, the frequency tends to increases as source approaches observer.

Please subscribe to promote our website. Subscription is free