Question

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)

Answer 1

Answer: 8

Speed of sound $=330m/s$
Calculate beat $f_{rea}$

$f_b=120\left[\left(\frac{330+10cos53^{\circ }}{330-30cos37^{\circ }}\right)-\left[\frac{330+10}{330}\right]\right]=120\left[\frac{336}{306}-\frac{34}{33}\right]=8.128Hz$