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]

Question

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] (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Vsound=330 m/s f1=120[(330+10 sin 53°/330-30 cos 37°)]Hz f2=120[(330+10/330)]Hz Δ f=120×[(336/306)-(34/33)] =8.13 Hz

Vsound​=330m/s f1​=120[330−30cos37∘330+10sin53∘​]Hz f2​=120[330330+10​]Hz Δf=120×[306336​−3334​] =8.13Hz

$V_{so u n d} = 330 m / s$
$f_{1} = 120 [\frac{330 + 10 s in 5 3 ^{\circ}}{330 - 30 cos 3 7 ^{\circ}}] Hz$
$f_{2} = 120 [\frac{330 + 10}{330}] Hz$
$Δ f = 120 \times [\frac{336}{306} - \frac{34}{33}]$
$= 8.13 Hz$