15.8 A transverse harmonic wave on a string is described by yx, t=3.0sin36t+0.018x+π4 where x and y are in cm and t in sec. 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 origin?

(d) What is the least distance between two successive crests in the wave?

The equation of a progressive wave travelling from right to left 
is given by the displacement function: 
y x, t=asinωt+kx+ϕ ....i
The given equation is:
yx, t=3.0sin36t+0.018x+π4             ....ii
On comparing both the equations, we find that the equation ii
 represents a travelling wave, propagating from right to left. 
Now, using equations i and ii,
 ω = 36 rad/s and k = 0.018 m-1
ν=ω2π and λ=2πk
So the speed of the wave: v=νλ
Amplitude of the given wave, a=3 cm
Frequency of the given wave:
ν=ω2π=362×3.14=5.73 Hz
On comparing equations i and ii, we find that the initial phase angle, ϕ=π4.
The distance between two successive crests
 or troughs is equal to the wavelength of the wave. 
Wavelength of the wave is given by: