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  4. A train S 1, 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]

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Q. A train S 1, 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]Physics Question Image

JEE AdvancedJEE Advanced 2019

Solution:

$V_{sound}=330\,m/s$
$f_{1}=120\left[\frac{330+10\,sin\,53^{\circ}}{330-30\,cos\,37^{\circ}}\right]Hz$
$f_{2}=120\left[\frac{330+10}{330}\right]Hz$
$\Delta f=120\times\left[\frac{336}{306}-\frac{34}{33}\right]$
$=8.13\,Hz$

Solution Image