Question

A source of sound, producing a sinusoidal wave, is moving uniformly towards an observer at a velocity of $20\text{m/s}$. The observer is moving away from the source at a constant velocity of $10\text{m/s.}$ Frequency of sound is $200\text{Hz}$ and speed of sound in air is $340\text{m/s}$. How many times, in an interval of $10\text{sec}$, will the eardrums of the observer sense maximum change in pressure?

• A. $20$
• B. $206$
• C. $438$
• D. $4125$

Answer 1

The correct option is D $4125$

From the data given in the question, we can deduce that, source and observer are moving in the same direction as the direction of sound waves.

So, from equation of Doppler effect, we can write that

Apparent frequency received by observer, $f=f_0\left(\frac{v-v_o}{v-v_s}\right)$

Substituting the given data, we get

$f=200\left[\frac{340-10}{340-20}\right]=206.25\text{Hz}$

In each cycle, the change in pressure is maximum for $2$ times.

So, number of times for which maximum change in pressure is sensed by the observer in $10\text{s}$ is

$n=206.25\times 2\times 10=4125$