Equation of two simple harmonic waves are given by Y₁ = 2sin 8π(t/0.2 - x/2)m and Y₂ = 4sin 8π(t/0.16 - x/1.6)m then both waves have (a) same period (b) same frequency (c) same wavelength (d) same velocity

Answer: (d). Y₁: ω₁ = (8π)/(0.2) = 40π, k₁ = 8π/2 = 4π, so v₁ = 10 m/s. Y₂: ω₂ = (8π)/(0.16) = 50π, k₂ = (8π)/(1.6) = 5π, so v₂ = 10 m/s. Periods, frequencies and wavelengths differ; speeds are equal. So the answer is (d) same velocity.

Equation of two simple harmonic waves are given by Y₁ = 2sin 8π(t/0.2… | MHT CET 2021 (21 Sep, Shift 2)

Q66MHT CET 2021 · 21 SEP · SHIFT 2Easy

Progressive Wave Equation

Equation of two simple harmonic waves are given by $Y_1 = 2\sin 8\pi\left(\frac{t}{0.2} - \frac{x}{2}\right)\text{m}$ and $Y_2 = 4\sin 8\pi\left(\frac{t}{0.16} - \frac{x}{1.6}\right)\text{m}$ then both waves have

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Answer: (d)

$Y_1$ : $\omega_1 = \dfrac{8\pi}{0.2} = 40\pi$ , $k_1 = \dfrac{8\pi}{2} = 4\pi$ , so $v_1 = 10\text{ m/s}$ .
$Y_2$ : $\omega_2 = \dfrac{8\pi}{0.16} = 50\pi$ , $k_2 = \dfrac{8\pi}{1.6} = 5\pi$ , so $v_2 = 10\text{ m/s}$ .
Periods, frequencies and wavelengths differ; speeds are equal.
So the answer is (d) same velocity.

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Progressive Wave Equation question from MHT CET 2021 (21 Sep, Shift 2)

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