Question

A car moves towards a hill with speed $v_c$. It blows a horn of frequency f which is heard by an observer following the car with speed $v_0$ .The speed of sound in air is v.

• A. The wavelength of sound reaching the hill is $\frac{V}{f}$
  
• B. The wavelength of sound reaching the hill is $\frac{V-V_C}{f}$
• C. The wavelength of sound of horn directly reaching the observer is $\frac{V+V_C}{f}$
• D. The beat frequency observed by the observer is $\frac{2V_C(V+V_0)f}{V^2-V_C^2}$

Answer 1

Answer: (B), (C), (D)

The correct options are
B The wavelength of sound reaching the hill is $\frac{V-V_C}{f}$
C The wavelength of sound of horn directly reaching the observer is $\frac{V+V_C}{f}$
D The beat frequency observed by the observer is $\frac{2V_C(V+V_0)f}{V^2-V_C^2}$

Frequency of horn directly heard by observer $\frac{v+v_0}{v+v_c}f$
Frequency of echo $=\frac{v}{v+v_c}f$
Frequency of echo of horn as heard by observer.
$\frac{v}{v-v_c}f.\left(\frac{v+v_0}{v}\right)$
Frequency of Beats
$=(v+v_0)f\{\frac{1}{v-v_c}-\frac{1}{v+v_c}\}=\frac{2v_c(v+v_0)}{(v^2-v_c^2)}f$