Question

The driver of a car travelling with speed $30\text{m/s}$ towards a cliff , sounds a horn of frequency $600\text{Hz}$. If the velocity of sound in air is $330\text{m/s}$, the frequency of sound heard by the driver reflected off the cliff is

[Assume, medium is stationary]

• A. $500\text{Hz}$
• B. $550\text{Hz}$
• C. $555.5\text{Hz}$
• D. $720\text{Hz}$

Answer 1

The correct option is D $720\text{Hz}$

Let $f_0$ be the frequency of sound heard by the observer, when both the source of sound and observer are at rest.
Let $v$ be the velocity of sound in the stationary medium, $v_s$ be the velocity of the source of sound and $v_0$ be the velocity of the observer.

Velocity of sound $v=330\text{m/s}$

When a source of sound is moving towards a stationary cliff, cliff will act as a mirror and the image of the sound source will be moving towards the observer.

Here, source of sound and the final observer are same $\therefore v_0=v_s=u\text{(say)}$

So, the apparent frequency heard by the observer due to reflected sound is given by

$f^{\prime }=\left(\frac{v+v_0}{v-v_s}\right)$

$\Rightarrow f^{\prime }=\left(\frac{v+u}{v-u}\right)f_0$

From the data given in the question,

$f_2=\frac{330+30}{330-30}\times 600\Rightarrow f_2=720\text{Hz}$