Question

For the wave described in Exercise 15.8, plot the displacement (y) versus (t) graphs for x = 0, 2 and 4 cm. What are the shapes of these graphs? In which aspects does the oscillatory motion in travelling wave differ from one point to another: amplitude, frequency or phase?

Answer 1

All the waves have different phases.

The given transverse harmonic wave is:

For x = 0, the equation reduces to:

Now, plotting y vs. t graphs using the different values of t, as listed in the given table.

t (s)	0
y (cm)		3		0		–3		0

For x = 0, x = 2, and x = 4, the phases of the three waves will get changed. This is because amplitude and frequency are invariant for any change in x. The y-t plots of the three waves are shown in the given figure.