Question

A whistle giving out $450\mathrm{Hz}$ approaches a stationary observer at a speed of $33{\mathrm{ms}}^{-1}$. We know that the velocity of sound is $330\mathrm{m}/\mathrm{s}$. What is the frequency heard by the observer in $\mathrm{Hz}$?

• A. $429$
• B. $409$
• C. $500$
• D. $517$

Answer 1

The correct option is C

$500$

Step 1: Given parameters

Velocity of sound ${\mathrm{V}}_{\mathrm{sound}}=330\mathrm{m}/\mathrm{s}$

Speed of source ${\mathrm{V}}_{\mathrm{source}}=33\mathrm{m}/\mathrm{s}$

Frequency of source $\mathrm{v}=450\mathrm{Hz}$

Step 3: Determine the frequency heard by the observer

Doppler effect when the source moves towards the stationary observer:

Apparent frequency heard by the observer ${\mathrm{v}}^{\text{'}}=\mathrm{v}\left[\frac{{\mathrm{V}}_{\text{sound}}}{{\mathrm{V}}_{\text{sound}}-{\mathrm{V}}_{\text{source}}}\right]$

$$\begin{gathered} {\mathrm{v}}^{\text{'}}=450\left[\frac{330}{330-33}\right] \\ {\mathrm{v}}^{\text{'}}=500\mathrm{Hz} \end{gathered}$$

Therefore, the frequency heard by the observer is $\mathbf{500}\mathbf{}\mathbf{Hz}$.

Hence, option (C) is correct.