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 – υ t or x + v t, i.e. y = f (x ± υ t). Is the converse true? Examine if the following functions for y can possibly represent a travelling wave :
(a) (x – υ t )²
(b) log [(x + υ t)/x0]
(c) 1/(x + υt)
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 – υ t or x + v t, i.e. y = f (x ± υ t). Is the converse true? Examine if the following functions for y can possibly represent a travelling wave :
(a) (x – υ t )²
(b) log [(x + υ t)/x0]
(c) 1/(x + υt)
The converse of the given condition is not true for the function.
For a function to represents a travelling wave, the function should be finite at everywhere and at all times.
(a)
At x=0 and t=0,
( x−vt ) 2 =∞
So, it cannot represent a travelling wave.
(b)
At x=0 and t=0,
log( x+vt x 0 )=log0 =∞
So, it cannot represent a travelling wave.
(c)
At x=0 and t=0,
1 x+vt = 1 0 =∞
So, it cannot represent a travelling wave.
Thus, the given functions are not representing a travelling wave.
The converse of the given condition is not true for the function.
For a function to represents a travelling wave, the function should be finite at everywhere and at all times.
(a)
At x=0 and t=0,
( x−vt ) 2 =∞
So, it cannot represent a travelling wave.
(b)
At x=0 and t=0,
log( x+vt x 0 )=log0 =∞
So, it cannot represent a travelling wave.
(c)
At x=0 and t=0,
1 x+vt = 1 0 =∞
So, it cannot represent a travelling wave.
Thus, the given functions are not representing a travelling wave.
