Question

A source of sound emits sound wave of frequency 'f' and moves towards an observer with a velocity $V/3$ where $V$ is the velocity of sound. If the observer moves away from the source with a velocity $V/5$ the apparent frequency heard by him will be ______.

• A. $\frac{15}{2}f$
• B. $\frac{8}{15}f$
• C. $\frac{6}{5}f$
• D. $\frac{15}{18}f$

Hint:

Doppler Sign Convention: "Towards = Higher frequency".
If observer moves towards, add to numerator.
If source moves towards, subtract from denominator.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
We use the Doppler Effect formula for sound: $f' = f \left( \frac{V \pm v_o}{V \mp v_s} \right)$.

Step 2: Formula Application:
Here, the observer is moving away ($-v_o$) and the source is moving towards the observer ($-v_s$). $v_o = V/5$ and $v_s = V/3$. $f' = f \left( \frac{V - V/5}{V - V/3} \right)$.

Step 3: Explanation:
$f' = f \left( \frac{4V/5}{2V/3} \right) = f \left( \frac{4}{5} \times \frac{3}{2} \right)$ $f' = f \left( \frac{12}{10} \right) = \frac{6}{5}f$.

Step 4: Final Answer:
The apparent frequency is $\frac{6}{5}f$.