Question:
Two sirens situated one km apart are producing sound of frequency \(330\) Hz. The observer starts moving from one siren to the other with a speed of \(2\) m/s. If the speed of sound is \(330\) m/s, What will be the beat frequency heard by the observer?
Two sirens situated one km apart are producing sound of frequency \(330\) Hz. The observer starts moving from one siren to the other with a speed of \(2\) m/s. If the speed of sound is \(330\) m/s, What will be the beat frequency heard by the observer?
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The observer moves away from one siren and toward the other. Find both apparent frequencies and subtract.
Updated On: Nov 12, 2026
- \(8\) Hz
- \(4\) Hz
- \(6\) Hz
- \(1\) Hz
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
The observer's motion changes the apparent frequency from each siren by the Doppler effect.
Step 2: Away from Siren 1
\(f_1=f\dfrac{v-u}{v}=330\times\dfrac{328}{330}=328\) Hz.
Step 3: Towards Siren 2
\(f_2=f\dfrac{v+u}{v}=330\times\dfrac{332}{330}=332\) Hz.
Step 4: Beat Frequency
\(f_2-f_1=332-328=4\) Hz.
Final Answer:
The observer hears 4 beats per second. \[ \boxed{\text{(B) }4\text{ Hz}} \]
The observer's motion changes the apparent frequency from each siren by the Doppler effect.
Step 2: Away from Siren 1
\(f_1=f\dfrac{v-u}{v}=330\times\dfrac{328}{330}=328\) Hz.
Step 3: Towards Siren 2
\(f_2=f\dfrac{v+u}{v}=330\times\dfrac{332}{330}=332\) Hz.
Step 4: Beat Frequency
\(f_2-f_1=332-328=4\) Hz.
Final Answer:
The observer hears 4 beats per second. \[ \boxed{\text{(B) }4\text{ Hz}} \]
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