Question:
A and B are two sources generating sound waves. A listener is situated at C. The frequency of the source at A is 500 Hz. A, now, moves towards C with a speed 4 m/s. The number of beats heard at C is 6. When A moves away from C with speed 4 m/s, the number of beats heard at C is 18. The speed of sound is 340 m/s. 
A and B are two sources generating sound waves. A listener is situated at C. The frequency of the source at A is 500 Hz. A, now, moves towards C with a speed 4 m/s. The number of beats heard at C is 6. When A moves away from C with speed 4 m/s, the number of beats heard at C is 18. The speed of sound is 340 m/s.
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Find the apparent frequency of A in the two cases (Doppler), then choose \(f_B\) that gives beat frequencies 6 and 18 respectively.
Updated On: Oct 31, 2026
- 500 Hz
- 506 Hz
- 512 Hz
- 494 Hz
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The Correct Option is C
Solution and Explanation
A moving towards C: \(f_1=500\times\frac{340}{340-4}=500\times\frac{340}{336}\approx506\) Hz.
A moving away from C: \(f_2=500\times\frac{340}{340+4}=500\times\frac{340}{344}\approx494\) Hz.
Beats \(|f_1-f_B|=6\) and \(|f_2-f_B|=18\).
Try \(f_B=512\) Hz: \(512-506=6\) and \(512-494=18\). Both conditions are satisfied. (500 Hz would give 6 and 6; 506 Hz would give 0; 494 Hz would give 12 and 0.)
Answer: (3) 512 Hz
A moving away from C: \(f_2=500\times\frac{340}{340+4}=500\times\frac{340}{344}\approx494\) Hz.
Beats \(|f_1-f_B|=6\) and \(|f_2-f_B|=18\).
Try \(f_B=512\) Hz: \(512-506=6\) and \(512-494=18\). Both conditions are satisfied. (500 Hz would give 6 and 6; 506 Hz would give 0; 494 Hz would give 12 and 0.)
Answer: (3) 512 Hz
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