For the wave, plot the displacement ( ) versus (t) graphs for 0,2 and .
(i) Give the shapes of these plots.
(ii) With respect to which aspects (amplitude, frequency or phase) does the oscillatory motion in a travelling wave differ from one point to another?

Given wave is,

…..(1)

Putting , the equation becomes:

…..(2)

Also,

secs

The displacement ( ) vs. (t) graphs using different values of t is,

Similarly, graphs are obtained for x=0, x=2, and x=4. The oscillatory motion in the travelling wave is different from each other only in terms of phase. Amplitude and frequency are invariant for any change in x. The y-t plots of the three waves are shown in the given figure: