$A$ progressive wave of frequency $50 \,Hz$ is travelling with velocity $350 \,m/s$ through a medium. The change in phase at a given time interval of $0.01 \,s$ is

$A$ progressive wave of frequency $500 \,Hz$ is travelling with a velocity of $360 \,ms^{-1}$. The distance between two points, having a phase difference of $60^{\circ}$, is ............. (in $\,m$)

$A$ progressive wave is given by $Y = 12 \sin (5t - 4x)$. On this wave,how far away are the two points having a phase difference of $90^{\circ}$?

The equation of a progressive wave is given by $y = a \sin \pi [\frac{t}{2} - \frac{x}{4}]$,where $t$ is in seconds and $x$ is in meters. The distance through which the wave moves in $8 \ s$ is .... $(m)$

$A$ 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?

The equation of a progressive wave is $Y = a \sin 2 \pi (n t - \frac{x}{5})$. The ratio of maximum particle velocity to wave velocity is