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

Answer 1

Answer: (B), (D)

The correct options are
B the wavelength of sound reaching the hill is $\frac{v-v_c}{f}$
D the beat frequency observed by the observer is $\frac{2v_c(v+v_o)f}{v^2-v_c^2}$

Speed of the car$={\upsilon }_c,$ frequency$=f$
Speed of the observer$={\upsilon }_o$
Let, the speed of sound$=\upsilon$
$V=\lambda f$ [$\lambda =$wavelength]
$\Rightarrow (\upsilon -{\upsilon }_c)=\lambda f$
$\Rightarrow \lambda =\frac{\upsilon -{\upsilon }_c}{f}$
The beat frequency observed by the observer
$f_b=\frac{(\upsilon +{\upsilon }_o)}{(\upsilon -{\upsilon }_c)}\times \frac{2f{\upsilon }_c}{(\upsilon +{\upsilon }_c)}=\frac{2{\upsilon }_c(\upsilon +{\upsilon }_c)f}{{\upsilon }^2-{\upsilon }_c^2}$