Question:
A siren emitting sound of frequency \(800\,Hz\) is going away from a static listener with a speed of \(30\,m/s\). Frequency of sound heard by the listener is \((\text{velocity of sound in air}=340\,m/s)\)
A siren emitting sound of frequency \(800\,Hz\) is going away from a static listener with a speed of \(30\,m/s\). Frequency of sound heard by the listener is \((\text{velocity of sound in air}=340\,m/s)\)
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When source moves away from listener, apparent frequency decreases and denominator becomes \(v+v_s\).
Updated On: May 7, 2026
- \(286.5\,Hz\)
- \(418.2\,Hz\)
- \(733.3\,Hz\)
- \(644.5\,Hz\)
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The Correct Option is C
Solution and Explanation
Concept:
When a sound source moves away from a stationary listener, the apparent frequency decreases. Formula is: \[ f'=\frac{v}{v+v_s}f \]
Step 1: Given: \[ f=800\,Hz \] \[ v=340\,m/s \] \[ v_s=30\,m/s \]
Step 2: Since the source is moving away: \[ f'=\frac{v}{v+v_s}f \]
Step 3: Substitute values: \[ f'=\frac{340}{340+30}\times 800 \] \[ f'=\frac{340}{370}\times 800 \]
Step 4: \[ f'=735.1\,Hz \]
Step 5: The closest option given is: \[ 733.3\,Hz \] \[ \boxed{733.3\,Hz} \]
When a sound source moves away from a stationary listener, the apparent frequency decreases. Formula is: \[ f'=\frac{v}{v+v_s}f \]
Step 1: Given: \[ f=800\,Hz \] \[ v=340\,m/s \] \[ v_s=30\,m/s \]
Step 2: Since the source is moving away: \[ f'=\frac{v}{v+v_s}f \]
Step 3: Substitute values: \[ f'=\frac{340}{340+30}\times 800 \] \[ f'=\frac{340}{370}\times 800 \]
Step 4: \[ f'=735.1\,Hz \]
Step 5: The closest option given is: \[ 733.3\,Hz \] \[ \boxed{733.3\,Hz} \]
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