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Wave Speed expression

A travelling ...

Question

A travelling wave is found to have the displacement by $y = 1 / {(1 + x)}^{2}$ at $t = 0$ , after $3 s e c$ the wave pulse is represented by equation $y = 1 / 1 + {(1 + x)}^{2}$ . The velocity of the wave is:

$1 m / s$

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$\frac{1}{3} m / s$

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$\frac{2}{3} m / s$

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$\frac{1}{4} m / s$

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Solution

The correct option is B
$\frac{1}{3} m / s$

Step 1. Given data :
Wave , $y = \frac{1}{{(1 + x)}^{2}}$ at $t = 0$
$y = \frac{1}{1 + {(1 + x)}^{2}}$ at $t = 3 s e c$
Step 2. Find the velocity of the wave is:
At $t = 0$
$y = \frac{1}{1 + x^{2}}$ ---- $(i)$
At $t = 3 s e c$ ,
$y = \frac{1}{1 + {(1 + x)}^{2}}$ ---- $(i i)$
The general form of traveling wave is given as below
$y = \frac{1}{1 + {(x \pm v t)}^{2}}$
comparing equation $(i i)$ and above general form of wave ,at $t = 3$ sec
$v t = 1$
$v = \frac{1}{t} v = \frac{1}{3} m / s e c$
Hence ,option (B) is correct .

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A travelling wave is found to have the displacement by y=1/(1+x)2at t=0, after3sec the wave pulse is represented by equationy=1/1+(1+x)2. The velocity of the wave is:

A travelling wave is found to have the displacement by $y = 1 / {(1 + x)}^{2}$ at $t = 0$ , after $3 s e c$ the wave pulse is represented by equation $y = 1 / 1 + {(1 + x)}^{2}$ . The velocity of the wave is: