15.5 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 [(x + vt)/x0]
(c) 1/(x + vt)
15.5 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 [(x + vt)/x0]
(c) 1/(x + vt)
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1 Answer
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(a) 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.
(b) For x =0 and t=0, the function = log 0 =
Since the function does not converge to a finite value for x =0 and t = 0, it represents a travelling wave.
(c) For x = 0 and t = 0, the function = =
Since the function does not converge to a finite value for x = 0 and t = 0, it does not represent a travelling wave.
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