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 $v$. Sound is reflected from the hill. Then:

• 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 $\frac{v+v_0}{f}$
• D. the beat frequency observed by the observer is $\frac{v_c(v+v_0)f}{v^2-{v_c}^2}$

Answer 1

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

Frequency of sound reaching the hill, $f^{\prime }$ = $\frac{v}{v-v_c}f$

So wavelength of sound reaching the hill = $\frac{v-v_c}{f}$

Frequency of sound directly heard by observer,$f^{{}^{\prime \prime \prime }}$ = $\frac{v+v_o}{v+v_c}f$

Wavelength of sound directly reaching observed = $\frac{v+v_c}{v+v_o}\frac{v}{f}$

Frequency of sound observed after refection from hill, f'' = $\frac{v+v_o}{v}{f}^{\prime }=\frac{v+v_o}{v-v_c}f$

So beat frequency = $|f^{{}^{\prime \prime \prime }}-f^{\prime \prime }|=\frac{2v_{c}f(v_o+v)}{v^2-v_c^2}$

Answer. B