Q.9: 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:
All the waves have different phases.
The given transverse harmonic wave is:
For x = 0, the equation reduces to:
Also,
ω = 2π/t = 36rad/s^{1}
∴ t = π/18 s
Now, plotting y vs. t graphs using the different values of t, as listed in the given table
t (s)

0

T/8

2T/7

3T/8

4T/8

5T/8

6T/8

7T/8

y (cm)

3/√2

3

3/√2

0

3/√2

–3

3/√2

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.