Waves

Question : 5 of 27

Marks: +1, -0

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 - vt)

(x + vt)

, i.e.

y = f (x \pm vt)

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

(a)

(x - vt)^2

(b)

\log\left[\frac{x + vt}{x_0}\right]

(c)

\frac{1}{x + vt}

Solution:

No, the converse is not true.

The basic requirement for a wave function to represent a travelling wave is that for all values of x and t, the wave function must have a finite value.

Out of the given functions for y, none of these satisfies this condition, so these functions do not represent a travelling wave.

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