The displacement of a wave is given by y = 0.002sin (100t + x) where ' x 'and ' y ' are in metre and ' t ' is in second. This represents a wave (a) of wavelength one metre (b) travelling with a velocity of 100 m/s in the negative x -direction (c) of frequency ((100)/(π)) Hz (d) travelling with a velocity of (50/π)m/s in the positive x -direction

Answer: (b). ω = 100 rad/s, k = 1 m⁻¹ λ = 2π m (not 1 m); f = (100)/(2π) = 50/π Hz (not (100)/(π)) v = (ω)/(k) = 100 m/s, and (ω t + kx) means motion along -x. So the answer is (b) 100 m/s in the negative x -direction.

The displacement of a wave is given by y = 0.002sin (100t + x) where… | MHT CET 2024 (3 May, Shift 1)

Q38MHT CET 2024 · 3 MAY · SHIFT 1Easy

Progressive Wave Equation

The displacement of a wave is given by $y = 0.002\sin(100t + x)$ where ' $x$ 'and ' $y$ ' are in metre and ' $t$ ' is in second. This represents a wave

Show answer and solution

Answer: (b)

$\omega = 100\text{ rad/s}$ , $k = 1\text{ m}^{-1}$
$\lambda = 2\pi\text{ m}$ (not 1 m); $f = \dfrac{100}{2\pi} = \dfrac{50}{\pi}\text{ Hz}$ (not $\dfrac{100}{\pi}$ )
$v = \dfrac{\omega}{k} = 100\text{ m/s}$ , and $(\omega t + kx)$ means motion along $-x$ .
So the answer is (b) $100\text{ m/s}$ in the negative $x$ -direction.

Report a mistake

Progressive Wave Equation question from MHT CET 2024 (3 May, Shift 1)

More questions on Progressive Wave Equation