$A$ transverse harmonic wave on a string is described by $y(x, t) = 3.0 \sin (36t + 0.018x + \pi/4)$,where $x$ and $y$ are in $cm$ and $t$ is 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 origin?
$(d)$ What is the least distance between two successive crests in the wave?

(A) The standard equation for a progressive wave is $y(x, t) = a \sin (\omega t + kx + \phi)$.
Comparing this with $y(x, t) = 3.0 \sin (36t + 0.018x + \pi/4)$:
$(a)$ Since the equation is of the form $f(ax + bt)$,it represents a travelling wave. Because the sign between $t$ and $x$ is positive,it propagates from right to left (negative $x$-direction). The speed $v = \omega/k = 36 / 0.018 = 2000 \, cm/s = 20 \, m/s$.
$(b)$ Amplitude $a = 3.0 \, cm$. Frequency $\nu = \omega / (2\pi) = 36 / (2 \times 3.1416) \approx 5.73 \, Hz$.
$(c)$ The initial phase at the origin $(x=0, t=0)$ is $\phi = \pi/4 \, rad$.
$(d)$ The distance between two successive crests is the wavelength $\lambda = 2\pi / k = 2 \times 3.1416 / 0.018 \approx 349 \, cm = 3.49 \, m$.