Question

An observer moves towards a stationary source of sound with a speed$1/5^{th}$ of speed of sound . the wavelength and frequency of the source emitted are $\lambda$ and f respectively. The apparent frequency recorded by the observer.

Answer 1

A whistle revolves in a circles of radius $R=0.5m$ with $w=20rad/s$

Observer hears the lowest frequency (striller sound) when source approaches towards him linearly (at $A$) as he is stationery due to doppler's effect

At $A$ velocity sources

$v_s=Rw$ (for circular motion)

$=0.5\times 20$

$\Rightarrow v_s=10m/s$

Given that original frequency of source $v=385Hz$ and speed of sound in air $=340m/s\left(v_s\right)$

Thus by doppler's effect apparent frequency:

$v^{\prime }=v\left(\frac{v}{v-v_s}\right)$ [observer stationery source moving towards him]

$=385\times \left(\frac{340}{340-10}\right)$

$v=396.7Hz$