JEE Advance - Physics (2019 - Paper 1 Offline - No. 18)
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 ............ .]
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 ............ .]
Answer
8.13
Explanation
Vsound = 330 m/s
$${f_1} = 120\left[ {{{330 + 10\,\cos \,53^\circ } \over {330 - 30\,\cos 37^\circ }}} \right]Hz$$
$${f_2} = 120\left[ {{{330 + 10} \over {330}}} \right]Hz$$
$$\Delta f = ({f_2} - {f_1}) = 120 \times \left[ {{{336} \over {306}} - {{34} \over {33}}} \right] = 8.13Hz$$
$${f_1} = 120\left[ {{{330 + 10\,\cos \,53^\circ } \over {330 - 30\,\cos 37^\circ }}} \right]Hz$$
$${f_2} = 120\left[ {{{330 + 10} \over {330}}} \right]Hz$$
$$\Delta f = ({f_2} - {f_1}) = 120 \times \left[ {{{336} \over {306}} - {{34} \over {33}}} \right] = 8.13Hz$$
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