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 obsreved 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 obsreved 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:

$=(v+v_0)f\{\frac{1}{v-v_c}-\frac{1}{v+v_c}\}=\frac{2v_c(v+v_0)}{(v^2-v_c^2)}f$