Question 40: Waves

Question

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 120 Hz. When O is 600 m away from 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 ............ .]

Accepted Answer

V
sound
= 330 m/s
$${f_1} = 120\left[ {{{330 + 10\,\cos \,53^\circ } \over {330 - 30\,\cos 37^\circ }}} ight]Hz$$
$${f_2} = 120\left[ {{{330 + 10} \over {330}}} ight]Hz$$
$$\Delta f = ({f_2} - {f_1}) = 120 	imes \left[ {{{336} \over {306}} - {{34} \over {33}}} ight] = 8.13Hz$$

Waves

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