If 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 metre and t in second. The wave function representing the pulse at time t, if the pulse is propagating along positive x-axis with speed 2 m/s is $y = \frac{10}{(x - 2 t)^{2} + p}$ . What is the value of p?

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Solution

The correct option is C 2
Wave equation at $t = 0$ , $\Rightarrow y = \frac{10}{x^{2} + 2}$ ........(1)
Wave equation as a function of time, $\Rightarrow y = \frac{10}{(x - 2 t)^{2} + p}$ ........(2)
Putting $t = 0$ in equation (2), we get $y = \frac{10}{x^{2} + p}$ .......(3)
Comparing (1) and (3) we get $p = 2$

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If at t = 0, a travelling wave pulse on a string is described by the function, y=10(x2+2). Here, x and y are in metre and t in second. The wave function representing the pulse at time t, if the pulse is propagating along positive x-axis with speed 2 m/s is y=10(x−2t)2+p. What is the value of p?

The correct option is C 2Wave equation at t=0, ⇒y=10x2+2 ........(1)Wave equation as a function of time, ⇒y=10(x−2t)2+p ........(2)Putting t=0 in equation (2), we get y=10x2+p .......(3)Comparing (1) and (3) we get p=2