Question:
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 is \(3n_{0}\), the velocity of the source \((V_{s})\) is equal to
[ V = Velocity of sound in air]
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 is \(3n_{0}\), the velocity of the source \((V_{s})\) is equal to
[ V = Velocity of sound in air]
[ V = Velocity of sound in air]
Show Hint
Use the Doppler formula for an approaching source with the heard frequency equal to three times the original.
Updated On: Nov 12, 2026
- \(2V\)
- \(\frac{2V}{3}\)
- \(\frac{V}{2}\)
- \(\frac{V}{3}\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
For a source approaching a stationary listener, the heard frequency is \(n=n_0\dfrac{V}{V-V_s}\).
Step 2: Substitute
\(3n_0=n_0\dfrac{V}{V-V_s}\Rightarrow V-V_s=\dfrac{V}{3}\)
Step 3: Solve
\(V_s=V-\dfrac{V}{3}=\dfrac{2V}{3}\)
Final Answer:
The source velocity is \(\dfrac{2V}{3}\). \[ \boxed{\text{(B) }\dfrac{2V}{3}} \]
For a source approaching a stationary listener, the heard frequency is \(n=n_0\dfrac{V}{V-V_s}\).
Step 2: Substitute
\(3n_0=n_0\dfrac{V}{V-V_s}\Rightarrow V-V_s=\dfrac{V}{3}\)
Step 3: Solve
\(V_s=V-\dfrac{V}{3}=\dfrac{2V}{3}\)
Final Answer:
The source velocity is \(\dfrac{2V}{3}\). \[ \boxed{\text{(B) }\dfrac{2V}{3}} \]
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