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Wave Speed

The amplitude...

Question

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

A

1 m / s

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B

1.5 m / s

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C

0.5 m / s

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D

2 m / s

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Solution

The correct option is D $0.5 m / s$
From the given $y (x)$ equations at two different times we can see that the value of y is maximum $(= 1 m)$ at $x = 0$ at $t = 0$ and at $x = 1$ at $t = 2$ .
So, the peak of the wave pulse has travelled a distance of $1 m$ (from $x = 0$ to $x = 1$ ) in $2 s$ along positive x - direction.
Hence, the wave velocity is:
$v = \frac{1}{2} = 0.5 m / s$
The correct answer is $O p t i o n C : 0.5 m / s$

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