### Waves - Result Question 74

#### 76. 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) $v / 4$

## Show Answer

#### Answer:

Correct Answer: 76. (c)

Solution:

- (c) Let $f^{\prime}$ be the frequency of sound heard by cliff.

$ \begin{equation*} \therefore f=\frac{v f}{v-v_c} \tag{1} \end{equation*} $

Now, for the reflected wave, 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 $\frac{v}{3}=v_c$