Answer to Question #164234 in Optics for Tary

Question

Deduce expressions for the frequency heard by an observer

(a.) when he is stationary and a source of sound is moving towards him and

(b.) when he is moving towards a stationary source of sound.

      Explain your reasoning carefully in each case.

Answer 1

Answer

a) according to concepts and theory

frequency of observer

$f_0=\frac{v}{\lambda_{eff}}\\=\frac{v}{vT-v_sT}$

s indicates for source and 0 for observer.

T=$\frac{1}{f_s}$

when he is stationary and a source of sound is moving towards him then

$f_0=\frac{v}{v-v_s}f_s$

b) similiarly

when he is moving towards a stationary source of sound

Then frequency of observer

Is given as

$f_0=\frac{v+v_s}{v}\frac{1}{T}\\=\frac{v+v_s}{v}f_s$