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At t = 0 a travelling wave pulse on a string is described by the function $y = \frac{10}{x^{2} + 2}$ here x and y are in meter and t in second. What will be the wave function representing the pulse at time t, if the pulse is propagating along the positive x-axis with speed 2 m/s ?

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$y = \frac{10}{{(x^{2} + 2 y)}^{2} + 2}$

$y = \frac{10}{{(x^{2} + 2 t)}^{2} + 2}$

$y = \frac{10}{(x - 2 t)^{2} + 2}$

$y = \frac{10}{(x + 2 t)^{2} + 2 t}$

answer is C.

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Detailed Solution

Replace x by $(x - v t) i,e., x - 2 t$
$\Rightarrow y = \frac{10}{(x - 2 t)^{2} + 2}$

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