You have learnt that a travelling wave in one dimension is repres… - Vidyadip

Question

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 ± v t). Is the converse true? Examine if the following functions for y can possibly represent a travelling wave:

(x – vt)²
log[(x + vt)/x₀]
1/(x + vt)

✓

Answer

No, the converse is not true. The basic requirements for a wave function to represent a travelling wave is that for all values of x and t, wave function must have finite value.
Out of the given functions for y, no one satisfies this condition. Therefore, none can represent a travelling wave.

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