What is a progressive wave?

The equation of a progressive wave is given by $y = 0.2 \cos \pi (0.04t + 0.02x - \frac{\pi}{6})$. The distance is expressed in $cm$ and time in seconds. What will be the minimum distance between two particles having a phase difference of $\pi / 2$ in $cm$?

$A$ wave is represented by $x = 0.4 \cos \left(8t - \frac{y}{2}\right)$ where $x$ and $y$ are in meters and $t$ is in seconds. The speed of the wave is

$A$ 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

$y=3 \sin \pi\left(\frac{t}{2}-\frac{x}{4}\right)$ represents an equation of a progressive wave,where $t$ is in $s$ and $x$ is in $m$. The distance travelled by the wave in $5 \,s$ is (in $\,m$)

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