A car moves towards a hill with speed v_c. It blows a horn of fre… - Vidyadip

MCQ

A car moves towards a hill with speed $v_c$. It blows a horn of frequency $f$ which is heared 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 $\frac{{2{v_c}(v + {v_o})\,f}}{{{v^2} - v_c^2}}$
✓
both $(B)$ and $(C)$

✓

Answer

Correct option: D.

both $(B)$ and $(C)$

d
Speed of the car $=v_{c},$ frequency $=f$

Speed of the observer $=v_{o}$

Let, the speed of sound $=v$

$V=\lambda f[\lambda=\text { wavelength }]$

$\Rightarrow\left(v-v_{c}\right)=\lambda f$

$\Rightarrow \lambda=\frac{v-v_{c}}{f}$

The beat frequency observed by the observer $f_{b}=\frac{\left(v+v_{o}\right)}{\left(v-v_{c}\right)} \times \frac{2 f v_{c}}{\left(v+v_{c}\right)}=\frac{2 v_{c}\left(v+v_{c}\right) f}{v^{2}-v_{c}^{2}}$

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