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Question

(B) The car acts as a source moving towards a stationary hill with speed $v_c$. The wavelength of the sound waves emitted by the car and reaching the

Vedclass · Accepted Answer

The wavelength of sound reaching the hill is $\frac{v - v_c}{f}$.

Vedclass · Answer

(B) The car acts as a source moving towards a stationary hill with speed $v_c$. The wavelength of the sound waves emitted by the car and reaching the hill is given by $\lambda = \frac{v - v_c}{f}$.The sound reflects off the hill and acts as a source moving away from the observer. The frequency of the reflected sound heard by the observer is $f' = f \left( \frac{v + v_o}{v - v_c} \right)$.The frequency of the direct sound heard by the observer is $f'' = f \left( \frac{v + v_o}{v - v_c} \right)$.Wait,the beat frequency is the difference between the frequency of the reflected sound and the direct sound. The reflected sound frequency $f_{ref} = f \left( \frac{v + v_o}{v - v_c} \right)$ and the direct sound frequency $f_{dir} = f \left( \frac{v - v_o}{v - v_c} \right)$.The beat frequency $f_b = |f_{ref} - f_{dir}| = f \left( \frac{v + v_o}{v - v_c} - \frac{v - v_o}{v - v_c} \right) = f \left( \frac{2v_o}{v - v_c} \right)$.Re-evaluating the provided options,option $(B)$ is correct as the wavelength is $\frac{v - v_c}{f}$. Therefore,$(B)$ is the correct choice.

$A$ 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 $v_o$. The speed of sound in air is $v$.

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