The equation of a plane progressive wave is given by y = 5cos π(200t - x/150) where x and y are in cm and t is in second. The velocity of the wave is ________ m/s. (a) 120 (b) 150 (c) 200 (d) 300

Answer: (d). y = 5cos (200π t - (π)/(150)x): ω = 200π s⁻¹, k = (π)/(150) cm⁻¹. v = (ω)/(k) = 200 × 150 = 30000 cm/s = 300 m/s So the answer is (d) 300 m/s.

The equation of a plane progressive wave is given by y = 5cos π(200t… | JEE Main 2026 (2 Apr, Shift 1)

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Progressive Wave Equation

The equation of a plane progressive wave is given by $y = 5\cos\pi\left(200t - \frac{x}{150}\right)$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is ________ m/s.

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Answer: (d)

$y = 5\cos\left(200\pi t - \dfrac{\pi}{150}x\right)$ : $\omega = 200\pi\text{ s}^{-1}$ , $k = \dfrac{\pi}{150}\text{ cm}^{-1}$ .
$v = \dfrac{\omega}{k} = 200 \times 150 = 30000\text{ cm/s} = 300\text{ m/s}$
So the answer is (d) $300\text{ m/s}$ .

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Progressive Wave Equation question from JEE Main 2026 (2 Apr, Shift 1)

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