For a progressive wave given by the equation $y = 4 \sin \frac{\pi}{2} (8t - \frac{x}{8}) \, cm$,what is the wave velocity and its direction?

Which of the following statements is incorrect during the propagation of a plane progressive mechanical wave?

The equation of a progressive wave is given by $y = A \cos 240(t - x/12)$,where $t$ is the time in seconds and $x$ is the distance in meters. The phase difference (in radians) between two positions $0.5 \, m$ apart is:

The equation of a progressive wave is given by $y = a \sin \pi (40t - x)$,where $a$ and $x$ are in meters and $t$ is in seconds. The velocity of the wave is ..... $m/s$.

The displacement of a plane progressive wave in a medium, travelling towards the positive $x$-axis with a velocity of $4 \ m/s$, at $t=0$ is given by $y=3 \sin 2 \pi (-x/3)$. The expression for the displacement at a later time $t=4 \ s$ will be:

$A$ 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?