Two loudspeakers are emitting sound waves of wavelength μ with an initial phase difference of 2π. At what minimum distance from O on line AB will one hear a maxima?

Δϕ=2nπ ⇒2π+λ2πd sin θ=2nπ;λ2πd sin θ=(2n−21)πsin θ=(2n−21)2dλ=21×2×3λλ=121⇒100λ2y=121144y2=(100λ)2;y≈12100λ=325λ

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Two loudspeakers are emitting sound waves of wavelength with

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Two loudspeakers are emitting sound waves of wavelength $μ$ with an initial phase difference of $\frac{π}{2}$ . At what minimum distance from O on line AB will one hear a maxima?

25 λ

\frac{100 λ}{15}

\frac{25 λ}{3}

50 λ

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Two loudspeakers are emitting sound waves of wavelength

μ

with an initial phase difference of

\frac{π}{2}

. At what minimum distance from O on line AB will one hear a maxima?

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

$Δ ϕ = 2 nπ \Rightarrow \frac{π}{2} + \frac{2 π}{λ} d s in θ = 2 nπ; \frac{2 π}{λ} d s in θ = (2 n - \frac{1}{2}) π$

$s in θ = (2 n - \frac{1}{2}) \frac{λ}{2 d} = \frac{1}{2} \times \frac{λ}{2 \times 3 λ} = \frac{1}{12} \Rightarrow \frac{y}{100 λ ^{2}} = \frac{1}{12}$

$144 y^{2} = (100 λ)^{2}; y \approx \frac{100 λ}{12} = \frac{25 λ}{3}$

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Question Text	Two loudspeakers are emitting sound waves of wavelength $μ$ with an initial phase difference of $\frac{π}{2}$ . At what minimum distance from O on line AB will one hear a maxima?
Answer Type	Text solution:1
Upvotes	151

Two loudspeakers are emitting sound waves of wavelength μ with an initial phase difference of 2π​. At what minimum distance from O on line AB will one hear a maxima?

Text solutionVerified

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Two loudspeakers are emitting sound waves of wavelength $μ$ with an initial phase difference of $\frac{π}{2}$ . At what minimum distance from O on line AB will one hear a maxima?