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

Δ ϕ = 2 n π ⇒ π 2 + 2 π λ d sin ⁡ θ = 2 n π 2 π λ d sin ⁡ θ = 2 n - 1 2 π s i n θ = 2 n - 1 2 λ 2 d = 1 2 × λ 2 × 3 λ = 1 12 ⇒ y 100 λ 2 = 1 12 144 y 2 = 100 λ 2 y ≈ 100 λ 12 = 25 λ 3

Physics - Sound Wave Question with Solution | TestHub

PhysicsSound WaveInterferenceHard2 minPYQ_2020

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$2$ 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 maxima?

Options:

Answer:

Solution:

$Δ ϕ = 2 n π$

$\Rightarrow \frac{π}{2} + \frac{2 π}{λ} d \sin θ = 2 n π$

$\frac{2 π}{λ} d \sin θ = (2 n - \frac{1}{2}) π$

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

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

$144 y^{2} = {(100 λ)}^{2}$

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

Stream:JEESubject:PhysicsTopic:Sound WaveSubtopic:Interference

⏱ 2mℹ️ Source: PYQ_2020

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