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

Distance travelled by a progressive wave having wavelength $\lambda$ and frequency $\nu$ in time $t$ is ......

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:

$A$ 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 .... $(m)$

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.