Question

A boy with a radio, playing a music at a frequency f is moving towards a wall with velocity v${}_b$ . A motorist is following the boy with a speed $v_m$.The expression for the beat frequency heard by the motorist, if the speed of sound is v, is

• A. $(\frac{v+v_m}{v+v_b})f$
• B. $\frac{v+v_m}{v-v_b}f$
• C. $\frac{2v_b(v+v_m)}{v^2-v_b^2}f$
• D. $\frac{2v_m(v+v_b)}{(v^2-v_m^2)}f$

Answer 1

Answer: (C)

$\frac{2v_b(v+v_m)}{v^2-v_b^2}f$

The apparent frequency of the sound to the motorist is:

$n_1=f\frac{V+V_m}{V+V_b}$. Now the doppler frequency of the actual sound to the boy is:

$n_2=f\frac{V}{V-V_b}$. The apparent frequency of the reflected sound to the motorist is:

$n_3=n_2\frac{V+V_m}{V}$. So the beat frequency will be:

$n_3-n_2=\frac{2v_b(v+v_m)}{v^2-v_b^2}f$