Question 11 Mark
You have learnt that a travelling wave in one dimension is represented by a function $y=f(x, t)$ where $x$ and $t$ must appear in the combination $x-v t$ or $x+v t$, i.e. $y=f(x \pm v t)$. Is the converse true? Examine if the following functions for $y$ can possibly represent a travelling wave :
(a) $(x-v t)^2$$\quad$$\quad$(b) $\log \frac{(x+v t)}{x_0}$$\quad$$\quad$(c) $\frac{1}{(x+v t)}$
(a) $(x-v t)^2$$\quad$$\quad$(b) $\log \frac{(x+v t)}{x_0}$$\quad$$\quad$(c) $\frac{1}{(x+v t)}$
Answer
View full question & answer→No, the converse is not true. It is basic restriction to represent progressive wave is that X and t. The value of the wave function should be limited for all values. None of the given functions satisfy this condition. For this reason these function not exibit progressive waves.
