Wave Motion 1 Question 14

14. The amplitude of a wave disturbance travelling in the positive $x$-direction is given by $y=\frac{1}{(1+x)^{2}}$ at time $t=0$ and by $y=\frac{1}{\left[1+(x-1)^{2}\right]}$ at $t=2 s$, where $x$ and $y$ are in metre. The shape of the wave disturbance does not change during the propagation. The velocity of the wave is ….. $m / s$.

(1990, 2M)

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Answer:

Correct Answer: 14. $2 \pi v A, 4 \pi^{2} v^{2} A$

Solution:

  1. In the question, it is given that the shape of the wave disturbance does not change, while in the opinion of author this is not true.

From the function, $y=\frac{1}{(1+x)^{2}}$, we can see that, at $x=-1, y=\infty$.

Whereas from the second function, $y=\frac{1}{\left[1+(x-1)^{2}\right]}$ we don’t get any point where $y=\infty$.

So, how can we say that shape has not changed.



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