A train S1, moving with a uniform velocity of 108 km / h, approac… - Vidyadip

MCQ

A train $S1$, 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
$5$
✓
$8$
C
$7$
D
$9$

✓

Answer

Correct option: B.

$8$

b
Frequency observed by $O$ from $S _2$

$f _2=\frac{330+10}{330} \times 120=\frac{340}{330} \times 120=123.63 Hz$

frequency observed by $O$ from $S _1$

$f_1=\frac{330+6}{330-24} \times 120=\frac{336}{306} \times 120 \approx 131.76 Hz$

beat frequency $=131.76-123.63=8.128 \approx 8.12$ to $8.13 Hz$

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