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 :

(a) (x – vt )2

(b) log $[\frac{x + vt}{x_0} ]$

(c) $\frac{1}{(x + vt)}$

Answer 1

No;

Does not represent a wave Represents a wave Does not represent a wave The converse of the given statement is not true. The essential requirement for a function to represent a travelling wave is that it should remain finite for all values of x and t.

Explanation:

For x = 0 and t = 0, the function (x – vt) 2 becomes 0.

Hence, for x = 0 and t = 0, the function represents a point and not a wave.

For x = 0 and t = 0, the function

log $(\frac{x+vt}{x_0})=logo=∞$

Since the function does not converge to a finite value for x = 0 and t = 0, it represents a travelling wave.

For x = 0 and t = 0, the function

log $\frac{1}{x+vt}=\frac{1}{0}=∞$

Since the function does not converge to a finite value for x = 0 and t = 0, it does not represent a travelling wave.