For the wave $y(x, t) = 3.0 \sin (36 t + 0.018 x + \pi / 4)$,plot the displacement $(y)$ versus time $(t)$ graphs for $x = 0, 2$ and $4 \; cm$. What are the shapes of these graphs? In which aspects does the oscillatory motion in a travelling wave differ from one point to another: amplitude,frequency,or phase?

(N/A) The given transverse harmonic wave equation is $y(x, t) = 3.0 \sin (36 t + 0.018 x + \pi / 4)$.
For $x = 0, 2,$ and $4 \; cm$,the equations are:
$y(0, t) = 3.0 \sin (36 t + \pi / 4)$
$y(2, t) = 3.0 \sin (36 t + 0.036 + \pi / 4)$
$y(4, t) = 3.0 \sin (36 t + 0.072 + \pi / 4)$
The angular frequency is $\omega = 36 \; rad/s$,so the time period is $T = 2\pi / \omega = \pi / 18 \; s$.
The shapes of these graphs are sinusoidal. In a travelling wave,the amplitude and frequency remain constant for all points,but the phase changes from one point to another due to the $kx$ term in the wave equation.