Two sound waves each of wavelength ' λ ' and having the same amplitude ' A ' from two source ' S₁ ' and ' S₂ ' interfere at a point P. If the path difference, S₂P - S₁P = λ/3 then the amplitude of resultant wave at point ' P ' will be [cos (120°) = -0.5] (a) A (b) 2A (c) A/2 (d) 3A/2

Answer: (a). Phase difference φ = (2π)/(λ)·(λ)/(3) = 2π/3 = 120°. AR = √(A² + A² + 2A²cos 120°) = √(2A² - A²) AR = A So the answer is (a) A.

Two sound waves each of wavelength ' λ ' and having the same… | MHT CET 2024 (16 May, Shift 1)

Q35MHT CET 2024 · 16 MAY · SHIFT 1Easy

Superposition, Coherence & Intensity

Two sound waves each of wavelength ' $\lambda$ ' and having the same amplitude ' $A$ ' from two source ' $S_1$ ' and ' $S_2$ ' interfere at a point P. If the path difference, $S_2P - S_1P = \lambda/3$ then the amplitude of resultant wave at point ' P ' will be $[\cos(120^\circ) = -0.5]$

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Answer: (a)

Phase difference $\phi = \dfrac{2\pi}{\lambda}\cdot\dfrac{\lambda}{3} = \dfrac{2\pi}{3} = 120^\circ$ .
$A_R = \sqrt{A^2 + A^2 + 2A^2\cos120^\circ} = \sqrt{2A^2 - A^2}$
$A_R = A$
So the answer is (a) $A$ .

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