A transverse harmonic wave on a strin is decribed by
`y(x,t) = 3.0 sin (36 t + 0.018x + pi//4)`
Where `x` and `y` are in `cm` and `t` in `s`. The positive direction of `x` is from left to right.
(a) Is this a travelling wave or a stationary wave ?
If it is travelling, what are the speed and direction of its propagation ?
(b) What are its amplitude and frequency ?
(c) What is the initial phase at the starting point ?
What is the least distance between two successive crests in the wave ?

Explanation

The transverse harmonic wave is `y(x,t)=3.0sin[36t+0.018x+(pi)/(4)]`
for x=0,
`y(0,t)=3.0sin(36t+pi//4)`
Here, `omega=(2pi)/(T)=36,T=(2pi)/(36)=(pi)/(18)s`

For different values of t, we calculate y using equation (i). These values are tabulated below :
On plotting y versus t graph, we obtained a sinusoidal curve as shown in above figure.


Similar are obtained for x=2 cm and x=4 cm.
The oscillatory motion in travelling wave differs from one point to another only in terms of phase. Amplitude and frequency of oscillatory motion remain the same in all the three cases