Waves Ques 74
74. A car is moving towards a high cliff. The car driver sounds a horn of frequency $f$. The reflected sound heard by the driver has frequency $2 f$. If $v$ be the velocity of sound, then the velocity of the car, in the same velocity units, will be
[2004]
(a) $v / 2$
(b) $v / \sqrt{2}$
(c) $v / 3$
(d) $v / 4$
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Answer:
Correct Answer: 74.(c)
Solution:
- (c) Let $f^{\prime}$ be the frequency of sound heard by the cliff.
$ \begin{equation*} \therefore f=\frac{v f}{v-v_c} \tag{1} \end{equation*} $
Now, for the reflected wave, the cliff acts as a source,
$\therefore 2 f=\frac{f^{\prime}(v+v_c)}{v}$
$2 f=\frac{(v+v_c) f}{v-v_c}$
$\Rightarrow 2 v-2 v_c=v+v_c$ or $\frac{v}{3}=v_c$
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