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At t = 0, a transverse wave pulse travelling in the positive x direction with a speed of 2 m/s in a wire is described by the function $y = \frac{6}{x^{2}}$ , given that x $\neq$ 0. Transverse velocity of a particle at x = 2m and t = 2 seconds is:

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8 m/s

-8 m/s

3 m/s

-3 m/s

answer is B.

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Detailed Solution

$y (x, t = 0) = \frac{6}{x^{2}} then y (x, t) = \frac{6}{{(x - 2 t)}^{2}}$

$\Rightarrow \frac{\partial y}{\partial t} = \frac{24}{{(x - 2 t)}^{3}} at x = 2, t = 2$

$V_{y} = \frac{24}{{(- 2)}^{3}} = - 3 m / s$

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