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 - 6-x2 given that x-0- Transverse velocity of a particle at x-2 m and t-2 s isA- 3 m - s B- 8 m - sC- -8 m - sD- -3 m - s

The correct option is D –3 m/sy (x, t = 0) = 6/x^2then y (x, t)= 6/(x 2t)^2 The particle velocity is δ y/δ t = 24/(x 2t)^3 at x = 2, t =2 V_y = 24/( 2)^3 = ...

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Standard XII

Physics

Wave Equation

At t =0, a tr...

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

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