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Standard XIII

Physics

Wave Equation

At t = 0, a t...

Question

At t = 0, a transverse wave pulse travelling in the positive x direction with a speed of 2 m/s in a wire is described by the function $y = \frac{6}{x^{2}} g i v e n t h a t x \neq 0$ . Transverse velocity of a particle at x = 2 m and t = 2 s is

3 m/s

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–3 m/s

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8 m/s

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–8 m/s

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Solution

The correct option is B –3 m/s
$y (x, t = 0) = \frac{6}{x^{2}} t h e n y (x, t) = \frac{6}{(x - 2 t)^{2}} T h e p a r t i c l e v e l o c i t y i s \frac{δ y}{δ t} = \frac{24}{(x - 2 t)^{3}} a t x = 2, t = 2 V_{y} = \frac{24}{(- 2)^{3}} = - 3 m / s$

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Similar questions

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At t = 0, a transverse wave pulse travelling in the positive x direction with a speed of 2 m/s in a wire is described by the function y=6x2given that x≠0. Transverse velocity of a particle at x = 2 m and t = 2 s is

The correct option is B –3 m/sy(x,t=0)=6x2then y(x,t)=6(x−2t)2Theparticlevelocityisδyδt=24(x−2t)3at x=2, t=2Vy=24(−2)3=−3m/s

At t = 0, a transverse wave pulse travelling in the positive x direction with a speed of 2 m/s in a wire is described by the function $y = \frac{6}{x^{2}} g i v e n t h a t x \neq 0$ . Transverse velocity of a particle at x = 2 m and t = 2 s is

The correct option is B –3 m/s
$y (x, t = 0) = \frac{6}{x^{2}} t h e n y (x, t) = \frac{6}{(x - 2 t)^{2}} T h e p a r t i c l e v e l o c i t y i s \frac{δ y}{δ t} = \frac{24}{(x - 2 t)^{3}} a t x = 2, t = 2 V_{y} = \frac{24}{(- 2)^{3}} = - 3 m / s$