The displacement y of a particle in a medium can be expressed as, y = 10⁻⁶sin (100t + 20x + π/4) m where t is in second and x in meter. The speed of the wave is (a) 20 m/s (b) 5 m/s (c) 2000 m/s (d) 5π m/s

Answer: (b). ω = 100 rad/s, k = 20 m⁻¹ v = (ω)/(k) = 100/20 = 5 m/s So the answer is (b) 5 m/s.

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Progressive Wave Equation

The displacement $y$ of a particle in a medium can be expressed as, $y = 10^{-6}\sin\left(100t + 20x + \frac{\pi}{4}\right)\text{ m}$ where $t$ is in second and $x$ in meter. The speed of the wave is

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Answer: (b)

$\omega = 100\text{ rad/s}$ , $k = 20\text{ m}^{-1}$
$v = \dfrac{\omega}{k} = \dfrac{100}{20} = 5\text{ m/s}$
So the answer is (b) $5\text{ m/s}$ .

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Progressive Wave Equation question from JEE Main 2004 (AIEEE)

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