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At t = 0 a transverse wave pulse in a wire is described by the function $y = \frac{6}{x^{2} - 3}$ where $x$ and $y$ are in meter. The function $y (x, t)$ that describes this wave equation it is travelling in the positive x direction with a speed of 4.5 m/s is

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$y = \frac{6}{{(x - 4.5 t)}^{2} - 3}$

$y = \frac{6}{{(x + 4.5 t)}^{2} - 3}$

$y = \frac{6}{{(x - 4.5 t)}^{2} + 3}$

$y = \frac{6}{{(x + 4.5 t)}^{2} + 3}$

answer is D.

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Detailed Solution

$y (x, t) = \frac{a}{{(x \pm v t)}^{2} + b}$ is another form of progressive wave equation propagating with a speed $v .$
Negative sign to be taken for propagation along +x-axis and positive sign to be taken to propagation along –x-axis

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