What will be the change in phase of a wave due to reflection from a free support?

$A$ progressive wave travelling along the positive $x-$ direction is represented by $y(x, t) = A \sin(kx - \omega t + \phi)$. Its snapshot at $t = 0$ is given in the figure. For this wave,the phase $\phi$ is

Define wave speed.

$A$ transverse progressive wave on a stretched string has a velocity of $10\,m/s$ and a frequency of $100\,Hz$. The phase difference between two particles of the string which are $2.5\,cm$ apart will be:

The equation of a progressive wave is $y = 4 \sin(4 \pi t - 0.04 x + \pi / 3)$, where $x$ is in meters and $t$ is in seconds. The velocity of the wave is:

The equation of a wave traveling along the $x$-axis is given by $y(x, t) = 0.005 \cos(\alpha x - \beta t)$. If the wavelength and time period of the wave are $0.08 \ m$ and $2.0 \ s$ respectively,find the values of $\alpha$ and $\beta$ in appropriate units.