Q157 / 200 · MHT CET - Medical 2026 (22 April Shift 1) · Physics

A source of sound emitting a note of frequency $n_0$ is approaching a stationary listener. If the frequency of the note heard by the listener $3n_0$, the velocity of the source $(V_s)$ is equal to
[ V = Velocity of sound in air]

  • A
    $2V$
  • Correct answer
    B
    $\dfrac{2V}{3}$
  • C
    $\dfrac{V}{2}$
  • D
    $\dfrac{V}{3}$

Solution

Using the Doppler effect formula for a source approaching a stationary listener:

$n' = n_0 \left( \dfrac{V}{V - V_s} \right)$

Substituting the given values, $n' = 3n_0$:

$3n_0 = n_0 \left( \dfrac{V}{V - V_s} \right)$

$3 = \dfrac{V}{V - V_s}$

$3V - 3V_s = V$

$2V = 3V_s$

$V_s = \dfrac{2V}{3}$

Answer: $\dfrac{2V}{3}$

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

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