Question

A source of sound $S$ is moving with a velocity of $50m/s$ towards a stationary observer. The observer measures the frequency of the source as $1000Hz$ when source is moving towards observer. What will be the frequency of the source when it is moving away from the observer after crossing him? (Take the velocity of sound in air as $350m/s$)

• A. $750Hz$
• B. $857Hz$
• C. $1143Hz$
• D. $807Hz$

Answer 1

The correct option is A

$750Hz$

Step 1: Given data

Source velocity $v_s=50m/s$

Frequency when source is going towards observer $f_o^{,}=1000Hz$

Velocity of sound in air $v=350m/s$

Observer velocity, $v_o=0m/s$

Frequency heard by observer when source is going away $=f_o$

Frequency of source $=f_s$

Step 2: Find the frequency

When source is going towards observer, the observer frequency is given by doppler effect,

$$\begin{gathered} f_o^{,}=f_s\frac{v-v_o}{v-v_s} \\ 1000=f_s\frac{350-0}{350-50} \\ {f}_s=875.14Hz \end{gathered}$$

When source is going away from observer, the observer frequency is given by doppler effect

$$\begin{gathered} f_o=f_s\frac{v-v_o}{v+v_s} \\ {f}_o=875.14\frac{350-0}{350+50} \\ {f}_o=750Hz \end{gathered}$$

The frequency observed by the observer when the source is moving away from him is 750 Hz.

Hence, Option A is correct.