Two simple harmonic progressive waves have displacements y₁ = a₁sin ((2π x)/(λ) - ω t) and y₂ = a₂cos ((2π x)/(λ) - ω t + φ) What is the phase difference between two waves? (a) (φ + π/2) (b) φ (c) (φ - π/2) (d) (φ + π)

Answer: (a). Let θ = (2π x)/(λ) - ω t; then y₁ = a₁sin θ. y₂ = a₂cos (θ + φ) = a₂sin (θ + φ + π/2) Phase difference = φ + π/2 So the answer is (a).

Two simple harmonic progressive waves have displacements y₁ = a₁sin… | MHT CET 2024 (2 May, Shift 1)

Q45MHT CET 2024 · 2 MAY · SHIFT 1Easy

Progressive Wave Equation

Two simple harmonic progressive waves have displacements $y_1 = a_1\sin\left(\frac{2\pi x}{\lambda} - \omega t\right)$ and $y_2 = a_2\cos\left(\frac{2\pi x}{\lambda} - \omega t + \phi\right)$ What is the phase difference between two waves?

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Answer: (a)

Let $\theta = \frac{2\pi x}{\lambda} - \omega t$ ; then $y_1 = a_1\sin\theta$ .
$y_2 = a_2\cos(\theta + \phi) = a_2\sin\left(\theta + \phi + \frac{\pi}{2}\right)$
Phase difference $= \phi + \frac{\pi}{2}$
So the answer is (a).

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Progressive Wave Equation question from MHT CET 2024 (2 May, Shift 1)

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