Which of the following functions for y can ne | vedclass

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(A) function $y = f(x, t)$ represents a travelling wave if and only if it can be expressed in the form $f(x \pm vt)$,where $v$ is the wave speed.$(a)$

Vedclass · Accepted Answer

Only $(a)$

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(A) function $y = f(x, t)$ represents a travelling wave if and only if it can be expressed in the form $f(x \pm vt)$,where $v$ is the wave speed.$(a)$ $y = (x^2 - vt)^2$: This cannot be written in the form $f(x \pm vt)$ because the $x$ term is squared while the $vt$ term is linear. Thus,it cannot represent a travelling wave.$(b)$ $y = \log \left[ \frac{x+vt}{x_0} \right]$: This is of the form $f(x+vt)$. It represents a travelling wave.$(c)$ $y = e^{-\left( \frac{x+vt}{x_0} \right)^2}$: This is of the form $f(x+vt)$. It represents a travelling wave.$(d)$ $y = \frac{1}{x+vt}$: This is of the form $f(x+vt)$. It represents a travelling wave.Therefore,only $(a)$ cannot represent a travelling wave.

Which of the following functions for $y$ can never represent a travelling wave?

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