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Two tuning forks with natural frequencies of 340 Hz each move relative to a stationary observer. One fork moves away from the observer, while the other moves towards him at the same speed of the tuning fork.

Two tuning forks with natural frequencies of 340 Hz each move relative to a stationary observer. One fork moves away from the observer, while the other moves towards him at the same speed of the tuning fork.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
8 years ago
Hello Student,
Please find the answer to your question
The apparent frequency from tuning fork T1 as heard by the observer will be
236-1628_6.png
v1 = c/c – v x v . . . . . . . . . . . . . . . . . . . . . . . (i)
where c = velocity of sound
v = velocity of turning fork
The apparent frequency from tuning fork T2 as heard by the observer will be
v2 = c/c + v x v . . . . . . . . . . . . . . . . . (ii)
Given v1 – v2 = 3
∴ c x v [1/c – v – 1/ c + v] = 3 or, 3 = c x v x 2v/c2 – v2
Since, v < < c ∴ 3 = c x v x 2v/c2
∴ v = 3 x 340 x 340/340 x 340 x 2 = 1.5 m/s

Thanks
Aditi Chauhan
askIITians Faculty

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