The displacement due to a wave moving in the positive x - direction is given by y - 1-1- x2 at time t - 0 and by y - 1-1 - x - 12 at t - 2 second- where x and y are in metre- The velocity of the wave in m-s is

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Standard XII

Physics

Derivation of the Speed of Sound

The displacem...

Question

The displacement due to a wave moving in the positive x - direction is given by y = $\frac{1}{(1 + x^{2})}$ at time t = 0 and by y = $\frac{1}{1 + {(x - 1)}^{2}}$ at t = 2 second, where x and y are in metre. The velocity of the wave in m/s is

$0.5$

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Solution

The correct option is A
$0.5$

In a wave equation , x and t must be related in the form (x - vt)

We rewrite the given equations y = $\frac{1}{1 + {(x - v t)}^{2}}$

For t = 0 , this becomes y = $\frac{1}{(1 + x^{2})}$ , as given

For t = 2, this becomes y = $\frac{1}{[1 + (x - 2 v)^{2}]} = \frac{1}{[1 + (x - 1)^{2}]}$

$\Rightarrow$ 2v = 1 or v = 0.5 m/s

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The displacement due to a wave moving in the positive x - direction is given by y = 1(1+x2) at time t = 0 and by y = 11+(x−1)2 at t = 2 second, where x and y are in metre. The velocity of the wave in m/s is

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The displacement due to a wave moving in the positive x - direction is given by y = $\frac{1}{(1 + x^{2})}$ at time t = 0 and by y = $\frac{1}{1 + {(x - 1)}^{2}}$ at t = 2 second, where x and y are in metre. The velocity of the wave in m/s is