Question

At what speed should a source of sound move away from a stationary observer so that the observer finds the apparent frequency equal to half the original frequency?

• A. $v/2$
• B. $2v$
• C. $v/4$
• D. $v$

Hint:

Doppler sign conventions: The numerator deals with the observer (moves toward source = $+$, moves away = $-$). The denominator deals with the source (moves toward observer = $-$, moves away = $+$).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The Doppler effect formula for a moving source and stationary observer is $f' = f \left( \frac{v}{v \pm v_s} \right)$.

Step 2: Formula Application:
The frequency decreases ($f' = f/2$), so the source must be moving away from the observer. $\frac{f}{2} = f \left( \frac{v}{v + v_s} \right)$.

Step 3: Explanation:
$\frac{1}{2} = \frac{v}{v + v_s} \implies v + v_s = 2v$. $v_s = v$.

Step 4: Final Answer:
The source should move at speed $v$.