A train $S1$, moving with a uniform velocity of $108 km / h$, approaches another train $S 2$ standing on a platform. An observer $O$ moves with a uniform velocity of $36 km / h$ towards $S 2$, as shown in figure. Both the trains are blowing whistles of same frequency $120 Hz$. When $O$ is $600 m$ away from $S 2$ and distance between $S 1$ and $S 2$ is $800 m$, the number of beats heard by $O$ is. . . . . [Speed of the sound $=330 m / s$ ]
IIT 2019, Medium
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Frequency observed by $O$ from $S _2$
$f _2=\frac{330+10}{330} \times 120=\frac{340}{330} \times 120=123.63 Hz$
frequency observed by $O$ from $S _1$
$f_1=\frac{330+6}{330-24} \times 120=\frac{336}{306} \times 120 \approx 131.76 Hz$
beat frequency $=131.76-123.63=8.128 \approx 8.12$ to $8.13 Hz$
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