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  4. A train S1, moving with a uniform velocity of 108km/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 ] (Approximate the answer to the nearest integer) <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-e6lxtbowkqmyk4yn.jpg />

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Q. A train $S1,$ moving with a uniform velocity of $108km/h,$ 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 $=330m/s$ ] (Approximate the answer to the nearest integer)
Question

NTA AbhyasNTA Abhyas 2022

Solution:

Speed of sound $=330m/s$
Calculate beat $f_{r e a}$
Solution
$f_{b}=120\left[\left(\frac{330 + 10 cos 53 ^\circ }{330 - 30 cos 37 ^\circ }\right) - \left[\frac{330 + 10}{330}\right]\right]=120\left[\frac{336}{306} - \frac{34}{33}\right]=8.128Hz$