The driver of a car travelling with speed $30 \mathrm{~ms}^{-1}$ towards a hill sounds a horn of frequency $600 \mathrm{~Hz}$. If the velocity of sound in air is $330 \mathrm{~ms}^{-1}$, the frequency of reflected sound as heard by driver is

• A

  $550 \mathrm{~Hz}$
• B

  $555.5 \mathrm{~Hz}$
• Correct answer
  C

  $720 \mathrm{~Hz}$
• D

  $500 \mathrm{~Hz}$

Solution

Key Idea Apply Doppler's effect. Whenever there is a relative motion between a source of sound and the observer (listner), the frequency of sound heard by the observer is different from the actual frequency of sound emitted by source.

[for case I] $\quad \mathbf{n}^{\prime}=\frac{\mathrm{v}}{\mathrm{v}-30} \mathbf{n}$ [for case II] $n^{\prime \prime}=\frac{v+30}{v} n^{\prime}$ From Eqs. (i) and (ii), we get $$ \begin{aligned} \mathrm{n}^{\prime \prime}=\frac{\mathrm{v}+30}{\mathrm{v}-30} \mathrm{n} & =\frac{360}{300} \times 600 \\ & =720 \mathrm{~Hz} \end{aligned} $$

Hence, the correct answer is option: 'C'.