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

`y(x, t) = 3.0 sin (36t + 0.018 x + (pi)/(4))," "...(i)`
Comparing this equation with
`y(x, t) = r sin [(2pi )/(lambda) (vt + x) + phi_(0)]`
(a) Speed, `upsilon = (36)/(0.018) = 2000 cms^(-1)`
This is a travelling wave with a speed of 2000 cm `s^(-1)`from right to left.
(b) Amplitude = 3.0 cm
The equation (i) can be written as
`y(x, t) = 3 sin [0.018 ((36)/(0.018)t + x) + (pi)/(4)]`
We get
`(2pi)/(lambda) = 0.018`
`rArr" "lambda = (2pi)/(0.018)` cm
Frequency `= (upsilon)/(lambda) = (2000)/(2pi) xx 0.018 = 5.7 s^(-1)`
(c) Initial phase at the origin `= (pi)/(4)` radian
(d) Least distance between two successive crests is `lambda` and is given by
`lambda = (2pi)/(0.018) = (2 xx 3.14)/(0.018) = 348 cm ~~ 3.5 m`