The displacement function of a wave travelling along positive x-direction is y - 1-2 - 3x2 at t - 0 and by y - 1-2 - 3 x - 22 at t - 2s- where y and x are in metre- The velocity of the wave is

The correct option is B 1 m/sGiven: y(x,0)=12+3x^2 y(x,2)=12+3(x 2)^2 If v is the velocity of the wave then, y(x,t)=y(x vt,0) Therefore, ...

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Standard XII

Physics

Wave in Negative X-Direction

The displacem...

Question

The displacement function of a wave travelling along positive x-direction is $y = \frac{1}{2 + 3 x^{2}}$ at t = 0 and by $y = \frac{1}{2 + 3 (x - 2)^{2}}$ at t = 2s, where y and x are in metre. The velocity of the wave is

2 m/s

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0.5 m/s

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1 m/s

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3 m/s

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Solution

The correct option is B 1 m/s
Given:
$y (x, 0) = \frac{1}{2 + 3 x^{2}}$
$y (x, 2) = \frac{1}{2 + 3 {(x - 2)}^{2}}$
If $v$ is the velocity of the wave then,
$y (x, t) = y (x - v t, 0)$
Therefore,
$y (x, 2) = y (x - 2 v, 0)$
Replacing values we get
$\frac{1}{2 + 3 {(x - 2)}^{2}} = \frac{1}{2 + 3 {(x - 2 v)}^{2}}$
Comparing LHS and RHS,
$x - 2 = x - 2 v$
$v = 1 m / s$

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The displacement function of a wave travelling along positive x-direction is y=12+3x2 at t = 0 and by y=12+3(x−2)2 at t = 2s, where y and x are in metre. The velocity of the wave is

The correct option is B 1 m/sGiven:y(x,0)=12+3x2y(x,2)=12+3(x−2)2If v is the velocity of the wave then,y(x,t)=y(x−vt,0)Therefore, y(x,2)=y(x−2v,0)Replacing values we get12+3(x−2)2=12+3(x−2v)2Comparing LHS and RHS, x−2=x−2vv=1m/s

The displacement function of a wave travelling along positive x-direction is $y = \frac{1}{2 + 3 x^{2}}$ at t = 0 and by $y = \frac{1}{2 + 3 (x - 2)^{2}}$ at t = 2s, where y and x are in metre. The velocity of the wave is