The amplitude of a wave disturbance propagating in positive direction of x - a x i s is given by y = 1 1 + x 2 at t = 0 and by y = 1 1 + x - 1 2 at t = 2 s , where x and y are in meters. The shape of the wave disturbance does not change during propagation. The velocity of the wave is

In a wave equation, x and t must be related in the form ( x - v t ) . Therefore, we rewrite the given equation as y = 1 1 + x - v t 2 For t = 0 , it becomes y = 1 1 + x 2 And for t = 2 , it becomes y = 1 1 + x - 2 v 2 = 1 1 + x - 1 2 ∴ 2 v = 1 or v = 0.5 m s - 1

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PhysicsSound WaveMiscellaneousMedium2 minPYQ_2020

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The amplitude of a wave disturbance propagating in positive direction of $x - a x i s$ is given by $y = \frac{1}{1 + x^{2}}$ at $t = 0$ and by $y = \frac{1}{1 + {(x - 1)}^{2}}$ at $t = 2 s$ , where $x$ and $y$ are in meters. The shape of the wave disturbance does not change during propagation. The velocity of the wave is

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Solution:

In a wave equation, $x$ and $t$ must be related in the form $(x - v t)$ . Therefore, we rewrite the given equation as

$y = \frac{1}{1 + {(x - v t)}^{2}}$

For $t = 0,$ it becomes $y = \frac{1}{1 + x^{2}}$

And for $t = 2$ , it becomes

$y = \frac{1}{[1 + {(x - 2 v)}^{2}]} = \frac{1}{1 + {(x - 1)}^{2}}$

$∴ 2 v = 1$ or $v = 0.5 m s^{- 1}$

Stream:JEESubject:PhysicsTopic:Sound WaveSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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