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An observer observes two moving trains, ...

An observer observes two moving trains, one reaching the station and other leaving the station with equal speeds of `8 ms^(-1)`. If each train sounds its whistles with frequency 240 Hz, then calculate the number of beats heard by the observer.

Text Solution

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Observer is stationary
(i) Source (train) is moving towards an observer:
Apparent frequency due to train arriving station is `f_("in") = (f)/(1 - (v_(s))/(v)) = (240)/(1 - (8)/(330)) = 246` Hz
(ii) Source (train) is moving away form an observer:
Apparent frequency due to train leaving station is `f_("out") = (f)/((1 - (v_s)/(v))) = (240)/((1 - (8)/(330))) = 234` Hz
So the number of beats `= |f_("in") - f_("out") | = (246 - 234) = 12`
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