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) (λ)/(2π)(Φ - π/2) (d) (2πΦ)/(λ)

Answer: (b). Write Y₂ as a sine: cos θ = sin (θ + π/2), so Y₂ = a₂sin (ω t - (2π x)/(λ) + Φ + π/2). Phase difference Δφ = Φ + π/2 Path difference = (λ)/(2π)Δφ = (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 2026 (13 May, Shift 2)

Q12MHT CET 2026 · 13 MAY · SHIFT 2Easy

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)

Write $Y_2$ as a sine: $\cos\theta = \sin\left(\theta + \frac{\pi}{2}\right)$ , so $Y_2 = a_2\sin\left(\omega t - \frac{2\pi x}{\lambda} + \Phi + \frac{\pi}{2}\right)$ .
Phase difference $\Delta\phi = \Phi + \frac{\pi}{2}$
Path difference $= \frac{\lambda}{2\pi}\Delta\phi = \frac{\lambda}{2\pi}\left(\Phi + \frac{\pi}{2}\right)$
So the answer is (b).

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Progressive Wave Equation question from MHT CET 2026 (13 May, Shift 2)

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