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Q.

A train S1, moving with a uniform velocity of 108 km/h  approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36km/h towards S2 as shown in figure. Both the trains are blowing whistles of same frequency 120Hz. When O is 600m away from S2 and distance between S1 and S2 is 800m, the number of beats heard by O is_____[ Speed of the sound =330m/s]

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answer is 8.13.

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Detailed Solution

tan⁡θ1=800600=43⇒θ1=53∘ and   θ2=37∘Now, Let say  Freq. Heard fromm train at S2=f2f2=V+V0Vfs=330+10330×fs=340330fsNow, Let say  freq. Heard from train at S1=f1⇒f1=V+V0cos⁡θ1V−Vscos⁡θ2fs=330+10×35330−30×45fs=336306fsSo,  Beat freq =336306fs−340330fs=336306−340330×120=8.13Hz
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