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

Engineering

Physics

Interference of Sound Wave

Question

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

50 λ

25 λ

$\frac{25 λ}{3}$

$\frac{100 λ}{\sqrt{15}}$

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$Δϕ = 2 nπ$

$\Rightarrow \frac{π}{2} + \frac{2 π}{λ} dsinθ = 2 nπ$

$\frac{2 π}{λ} dsinθ = (2 n - \frac{1}{2}) π$

$sinθ = (2 n - \frac{1}{2}) \frac{λ}{2 d} = \frac{1}{2} \times \frac{λ}{2 \times 3 λ} = \frac{1}{12}$

$\Rightarrow \frac{y}{\sqrt{(100 λ)^{2}}} = \frac{1}{12}$

144y² = (100λ)²

$y \approx \frac{100 λ}{12} = \frac{25 λ}{3}$ .

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