A train S1, moving with a uniform velocity of 108 km/h, approaches another train S2 standing on a platform. An observer O moves with a uniform velocity of 36 km/h towards S2, as shown in figure. Both the trains are blowing whistles of same frequency 120Hz. When O is 600 m away form S2 and distance between S1 and S2 is 800 m, the number of beats heard by O is ....... [Speed of the sound = 330 m/s]

Answer

8.13

Explanation

For reflected sound we can assume it to be a case of source and observer approaching towards each other. If u is speed of car and `upsilon` is speed of sound then frequency received after reflection can be written as follows :
`f = f_(0) ((upsilon + u)/(v - u))`
Beat frequency can be written as follows :
`Delta f = f_(0) ((upsilon + u)/(upsilon - u)) - f_(0)`
`rArr" "Delta f = f_(0) (2u)/(upsilon - u)`
Substituting values we get the following :
`rArr" "Delta f = 492 xx ((2 xx 2)/(330 - 2)) = 6`