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JEE Mains · Physics · STD 11 - Waves and sound
- JEE Mains 2013
- Medium
- Numerical
\(A\) 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 \(340\,m/s.\) The frequency of the source at \(B\) is ..... \(Hz\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(C) \(512\)
Step-by-step Solution
Detailed explanation
\(Case\, 1:\) When source is moving towards stationary listener
apparent frequency \(\eta^{\prime}=\eta\left(\frac{\mathrm{v}}{\mathrm{v}-\mathrm{v}_{\mathrm{s}}}\right)\)
\(=500\left(\frac{340}{336}\right)=506 \mathrm{Hz}\)
\(Case\, 2:\) When source is moving away from the stationary listener
\(\eta^{\prime \prime}=\eta\left(\frac{v}{v+v_{s}}\right)=500\left(\frac{340}{344}\right)=494 \mathrm{Hz}\)
In case \(1\) rumber of beats heard is \(6\) and in
\(case\, 2\) number of beats heard is \(18\) therefore frequency of the source at \(\mathrm{B}=512 \mathrm{Hz}\)
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