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COE in SHM

Two trains ar...

Question

Two trains are moving on parallel track with $4 m / s$ in opposite direction each. What will be the number of beats heard by a person sitting in one of the train if both the trains blows whistle of $400 H z$ . $V_{s o u n d} = 340 m / s$ . The whistles were blown when they are facing one another :

4.7 b e a t s / s

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8.2 b e a t s / s

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7.9 b e a t s / s

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9.3 b e a t s / s

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Solution

The correct option is C $9.3 b e a t s / s$
One train will work as a source and other will work as a object
given that both trains are moving with velocity 4m/s ,
$V_{S o u r c e} = 4 m / s$ $V_{O b j e c t} = 4 m / s$
$f^{'} = f \frac{V_{s o u n d} + V_{o b j e c t}}{V_{s o u n d} - V_{s o u r c e}}$
$f^{'} = 400 \frac{340 + 4}{340 - 4}$

$= 400 \frac{344}{336} = 390.7 H z$
So beats = $f_{1} - f^{'} = 9.3 b e a t s / s$

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