Question

The speed of sound in air is $340m/s$. The speed with which a source of sound should move towards a stationary observer so that the apparent frequency becomes twice the original is

• A. $640m{s}^{-1}$
• B. $340m{s}^{-1}$
• C. $170m{s}^{-1}$
• D. $85m{s}^{-1}$

Answer 1

The correct option is C

$170m{s}^{-1}$

Step 1: Given Data

Given, the velocity of the sound in air, $v=340m/s$

The apparent frequency is twice the actual,

=$\frac{n^{\text{'}}}{n}=2$

where $n\text{'}$ is the frequency observed by the stationary observer (apparent frequency).

and, $n$ is the frequency produced by the moving source (original frequency).

Step 2: Formula Used

Here, the source is in motion and the observer is stationary, thus doppler's effect for this case gives:

$\frac{n^{\text{'}}}{n}=\left(\frac{v}{v-v_s}\right)$ ( $v_s$ is the velocity of the source)

Step 3: Solution

Putting the known value in the above formula, we get

$2=\frac{v}{v-v_s}$

$2=\frac{v}{v-v_s}$

$2v-2v_s=v$

$v_s=\frac{v}{2}$

$v_s=$$\frac{340m/s}{2}$$=170m/s$ is the rate at which a sound source should move towards a stationary observer.

Hence, option C is the correct answer.