Question

A train $S_1$ moving with a uniform velocity of $108km/h$ approaches another train $S_2$ standing on a platform. An observer $O$ moves with a uniform velocity of $36km/h$ towards $S_2$ as shown in figure. Both the trains are blowing whistles of same frequency $120Hz$. When O is $600m$ away from $S_2$ and distance between $S_1$ and $S_2$ is $800m$, the number of beats heard by O is . (Speed of the sound $=330m/s$)

Answer 1

Speed of sound $=330m/s$
Number of beats = frequency difference between the frequency observed by observer from $S_1$ and $S_2$, $f_b=120[\left(\frac{330+10\cos {53}^o}{330-30\cos {37}^o}\right)-\left(\frac{330+10}{330}\right)]=120[\frac{336}{306}-\frac{34}{33}]=8.128Hz$