$A$ 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

In the given progressive wave $y = 5 \sin(100\pi t + 0.4\pi x)$,where $y$ and $x$ are in $m$ and $t$ is in $s$. Find the:
$(a)$ Amplitude
$(b)$ Wavelength
$(c)$ Frequency
$(d)$ Wave velocity
$(e)$ Particle velocity amplitude.

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

The equation of a plane progressive wave is given by $y = 5 \cos \pi (200t - \frac{x}{150})$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is . . . . . . m/s.

$A$ 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 given by $y = 0.5 \sin(10t + x) \text{ m}$. What is the wave velocity in $\text{m/s}$?