With what velocity an observer should move relative to a stationary source so that a sound of triple the…

With what velocity an observer should move relative to a stationary source so that a sound of triple the frequency of source is heard by an observer?
  1. Same as velocity of sound towards the source.
  2. Same as velocity of sound away from the source.
  3. Half the velocity of sound towards the source.
  4. Twice the velocity of sound towards the source.

Solution

Applying Doppler's effect to sound waves, we can write, $n^{\prime}=n\left(\frac{v+v_0}{v}\right)=n\left(1+\frac{v_0}{v}\right)$. $\begin{array}{ll} & \mathrm{n}^{\prime}=3 n \quad \ldots . \text { (given) } \\ \therefore \quad & 3 n=n\left(1+\frac{v_0}{v}\right) \\ \therefore \quad & 3=1+\frac{v_0}{v} \\ \therefore \quad & \frac{v_0}{v}=2 \quad \Rightarrow v_0=2 v \end{array}$

Asked in: MHT CET 2024 (11 May Shift 1)

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