Question:
The source is emitting sound of frequency 'n'. A source and a listener both are moving towards each other with a speed equal to \(\left(\frac{V}{3}\right)\), where V is the speed of sound. The frequency heard by the listener will be
The source is emitting sound of frequency 'n'. A source and a listener both are moving towards each other with a speed equal to \(\left(\frac{V}{3}\right)\), where V is the speed of sound. The frequency heard by the listener will be
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Use the Doppler formula with both speeds in the favourable direction.
Updated On: Nov 12, 2026
- \(\frac{n}{3}\)
- \(\frac{n}{2}\)
- \(2n\)
- \(3n\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept
When source and listener move toward each other, \(n'=n\,\dfrac{V+v_L}{V-v_S}\).
Step 2: Substitute
\(v_L=v_S=\dfrac{V}{3}\)
\(n'=n\,\dfrac{V+V/3}{V-V/3}=n\,\dfrac{4/3}{2/3}\)
Step 3: Simplify
\(n'=2n\)
Final Answer:
The listener hears a frequency of 2n. \[ \boxed{\text{(C) }2n} \]
When source and listener move toward each other, \(n'=n\,\dfrac{V+v_L}{V-v_S}\).
Step 2: Substitute
\(v_L=v_S=\dfrac{V}{3}\)
\(n'=n\,\dfrac{V+V/3}{V-V/3}=n\,\dfrac{4/3}{2/3}\)
Step 3: Simplify
\(n'=2n\)
Final Answer:
The listener hears a frequency of 2n. \[ \boxed{\text{(C) }2n} \]
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