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Sound waves are passing through two routes-one in straight pat

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Sound waves are passing through two routes-one in straight path and the other along a semicircular path of radius $r$ and are again combined into one pipe and superposed as shown in the figure. If the velocity of sound waves in the pipe is $v$ , then frequencies of resultant waves of maximum amplitude will be integral multiples of

\frac{v}{r ( π - 2 )}

\frac{v}{r ( π - 1 )}

\frac{2 v}{r ( π - 1 )}

\frac{v}{r ( π + 1 )}

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Sound waves are passing through two routes-one in straight path and the other along a semicircular path of radius

r

and are again combined into one pipe and superposed as shown in the figure. If the velocity of sound waves in the pipe is

v

, then frequencies of resultant waves of maximum amplitude will be integral multiples of

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Text solutionVerified

Path difference between the sound waves traveling from path

I

and

II

Δ x = π r - 2 r

⟹

Δ x = r (π - 2)

Constructive interference results in the resultant waves of maximum amplitude.

For constructive interference

λ = Δ x

∴

λ = r (π - 2)

Frequency of resultant wave

ν = \frac{v}{λ} = \frac{v}{r ( π - 2 )}

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Question Text	Sound waves are passing through two routes-one in straight path and the other along a semicircular path of radius $r$ and are again combined into one pipe and superposed as shown in the figure. If the velocity of sound waves in the pipe is $v$ , then frequencies of resultant waves of maximum amplitude will be integral multiples of
Answer Type	Text solution:1
Upvotes	151