MHT CET · Physics · Waves and Sound
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?
- A Same as velocity of sound towards the source.
- B Same as velocity of sound away from the source.
- C Half the velocity of sound towards the source.
- D Twice the velocity of sound towards the source.
Answer & Solution
Correct Answer
(D) Twice the velocity of sound towards the source.
Step-by-step Solution
Detailed explanation
Applying Doppler's effect to sound waves, we can write, \(n^{\prime}=n\left(\frac{v+v_0}{v}\right)=n\left(1+\frac{v_0}{v}\right)\).
\(\begin{array}{ll}
& \mathrm{n}^{\prime}=3 n \quad \ldots . \text { (given) } \\
\therefore \quad & 3 n=n\left(1+\frac{v_0}{v}\right) \\
\therefore \quad & 3=1+\frac{v_0}{v} \\
\therefore \quad & \frac{v_0}{v}=2 \quad \Rightarrow v_0=2 v
\end{array}\)
\(\begin{array}{ll}
& \mathrm{n}^{\prime}=3 n \quad \ldots . \text { (given) } \\
\therefore \quad & 3 n=n\left(1+\frac{v_0}{v}\right) \\
\therefore \quad & 3=1+\frac{v_0}{v} \\
\therefore \quad & \frac{v_0}{v}=2 \quad \Rightarrow v_0=2 v
\end{array}\)
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