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?

Question

Philoid · Accepted Answer

Given:

Wave function, y = 3.0 sin (36 t + 0.018 x + π/4) …(1)

For x = 0, equation reduces to,

y = 3.0 sin (36 t + π/4) …(2)

w = 2π/T

T = 2π rad/36rad s^-1

T = π/18

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

In the same fashion we can also find the graph for x = 2 and x = 4, for these cases the phase will change.

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?