A travelling harmonic wave is represented by the equation y(x,t) = 10–3sin (50t + 2x), where, x and y are in metre and t is in seconds. Which of the following is a correct statement about the wave? (a) The wave is propagating along the positive x-axis with speed 100 ms–1 (b) The wave is propagating along the positive x-axis with speed 25 ms–1 (c) The wave is propagating along the negative x-axis with speed 25 ms–1 (d) The wave is propagating along the negative x-axis with speed 100 ms–1

Answer: (c). ω = 50 rad/s, k = 2 m⁻¹, so v = (ω)/(k) = 25 m/s. Form (ω t + kx) means the wave travels along -x. So the answer is (c) negative x -axis with speed 25 m s⁻¹.

A travelling harmonic wave is represented by the equation y(x,t) =… | JEE Main 2019 (12 Jan, Shift 1)

Q80JEE Main 2019 · 12 JAN · SHIFT 1Easy

Progressive Wave Equation

A travelling harmonic wave is represented by the equation y(x,t) = 10–3sin (50t + 2x), where, x and y are in metre and t is in seconds. Which of the following is a correct statement about the wave?

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Answer: (c)

$\omega = 50\text{ rad/s}$ , $k = 2\text{ m}^{-1}$ , so $v = \dfrac{\omega}{k} = 25\text{ m/s}$ .
Form $(\omega t + kx)$ means the wave travels along $-x$ .
So the answer is (c) negative $x$ -axis with speed $25\text{ m s}^{-1}$ .

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Progressive Wave Equation question from JEE Main 2019 (12 Jan, Shift 1)

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