The path difference between two waves Y₁ = a₁sin (ω t - (2π x)/(λ)) and Y₂ = a₂cos (ω t - (2π x)/(λ) + φ) is (a) (λφ)/(2π) (b) (λ)/(2π)(φ + π/2) (c) (2π)/(λ)(φ - π/2) (d) (2π)/(λ)φ

Answer: (b). Y₂ = a₂cos (θ + φ) = a₂sin (θ + φ + π/2) with θ = ω t - (2π x)/(λ). Phase difference = φ + π/2 Path difference = (λ)/(2π)(φ + π/2) So the answer is (b).

The path difference between two waves Y₁ = a₁sin (ω t - (2π x)/(λ))… | MHT CET 2024 (3 May, Shift 1)

Q44MHT CET 2024 · 3 MAY · SHIFT 1Easy

Progressive Wave Equation

The path difference between two waves $Y_1 = a_1\sin\left(\omega t - \frac{2\pi x}{\lambda}\right)$ and $Y_2 = a_2\cos\left(\omega t - \frac{2\pi x}{\lambda} + \phi\right)$ is

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Answer: (b)

$Y_2 = a_2\cos(\theta + \phi) = a_2\sin\left(\theta + \phi + \frac{\pi}{2}\right)$ with $\theta = \omega t - \frac{2\pi x}{\lambda}$ .
Phase difference $= \phi + \frac{\pi}{2}$
Path difference $= \frac{\lambda}{2\pi}\left(\phi + \frac{\pi}{2}\right)$
So the answer is (b).

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Progressive Wave Equation question from MHT CET 2024 (3 May, Shift 1)

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