Physics

Physics

Problem

14.5 You have learnt that a travelling wave in one dimension is represented by a function y=f(x,t)y=f(x, t) where xx and tt must appear in the combination x−vtx-v t or x+vtx+v t, i.e. y=f(x±vt)y=f(x \pm v t). Is the converse true? Examine if the following functions for yy can possibly represent a travelling wave : (a) (x−vt)2\quad(x-v t)^{2} (b) log⁡[(x+vt)/x0]\quad \log \left[(x+v t) / x_{0}\right] (c) 1/(x+vt)\quad 1 /(x+v t) (a) (x−vt)2\quad(x-v t)^{2} (b) log⁡[(x+vt)/x0]\quad \log \left[(x+v t) / x_{0}\right] (c) 1/(x+vt)\quad 1 /(x+v t)

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