If at $t = 0$ , a travelling wave pulse on a string is described by the function $Y = \frac{6}{x^{2} + 3}$ . What will be the wave function representing the pulse at time t, if the pulse is propagating along positive x-axis with speed $4 m / s$ ?

Y = \frac{6}{(x - 4 t)^{2} + 3}

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Y = \frac{6}{(x + 4 t)^{2} + 3}

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Y = \frac{6}{(x - t)^{2}}

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Y = \frac{6}{(x - t)^{2} + 12}

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Solution

The correct option is B $Y = \frac{6}{(x + 4 t)^{2} + 3}$
A wave traveling in positive x direction is given by,
$Y = f (x - v t)$
at t = 0, $Y = \frac{6}{x^{2} + 3}$
Therefore, replacing $x$ by $x - v t$ , we get
$Y (t) = \frac{6}{(x - v t)^{2} + 3}$
$\Rightarrow Y (t) = \frac{6}{(x - 4 t)^{2} + 3}$

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