For waves propagating in a medium,identify the property that is independent of the others.

$A$ travelling wave is described by the equation $y(x, t) = 0.05 \sin(8x - 4t) \; m$. The velocity of the wave is $..... \; m/s$ [all the quantities are in $SI$ units].

$A$ wave is propagating along the $x$-axis. The displacement of particles of the medium in the $z$-direction at $t = 0$ is given by: $z = \exp[-(x + 2)^2]$,where $x$ is in meters. At $t = 1 \ s$,the same wave disturbance is given by: $z = \exp[-(2 - x)^2]$. Then,the wave propagation velocity is:

$A$ wave is represented by the equation $y = 7\sin \{ \pi (2t - 2x) \} $ where $x$ is in metres and $t$ is in seconds. The velocity of the wave is ..... $m/s$.

$A$ simple harmonic progressive wave is represented by $y=A \sin (100 \pi t+3 x)$. The distance between two points on the wave at a phase difference of $\frac{\pi}{3}$ radian is

$A$ wave is represented by $x = 4 \cos \left(8t - \frac{y}{2}\right)$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The frequency of the wave (in $s^{-1}$) is .........