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Sound waves from a tuning fork A reach a point P by two separate paths ABP and ACP. When ACP is greater than ABP by 11.5 cm, there is silence at P. When the difference is 23 cm the sound becomes loudest at P and when 34.5 cm there is silence again and so on. Calculate the minimum frequency (in Hz) of the fork if the velocity of sound is taken to be 331.2 m/s.

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Sound waves from a tuning fork A reach a point P by two separate paths ABP and ACP. When ACP is greater than ABP by 11.5 cm, there is silence at P. When the difference is 23 cm the sound becomes loudest at P and when 34.5 cm there is silence again and so on. Calculate the minimum frequency (in Hz) of the fork if the velocity of sound is taken to be 331.2 m/s.

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Text solutionVerified

When path difference =

11.5 c m = \frac{λ}{2} (2 n - 1)

Because there is silence at

P

let

n = 1

11.5 = \frac{λ}{2}

So, at

\frac{2}{λ} 2

there will be maxima.

and yes at

23 c m

there is maxima, at

3 λ /2 = 34.5

There is minima, so,

λ = 23 c m

v = f λ

\frac{331.2}{23 \times 1 0 ^{- 2}} = f = 1440 Hz

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Question Text	Sound waves from a tuning fork A reach a point P by two separate paths ABP and ACP. When ACP is greater than ABP by 11.5 cm, there is silence at P. When the difference is 23 cm the sound becomes loudest at P and when 34.5 cm there is silence again and so on. Calculate the minimum frequency (in Hz) of the fork if the velocity of sound is taken to be 331.2 m/s.
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

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