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

When a sound wave of wavelength $\lambda$ is propagating in a medium, the maximum velocity of the particle is equal to the wave velocity. The amplitude of the wave is:

For a wave equation $Y = Y_0 \sin 2\pi \left( ft - \frac{x}{\lambda} \right) \text{ cm}$,the condition for the maximum particle velocity to be four times the wave velocity is:

$A$ plane progressive wave is given by $y = 2 \cos 2 \pi (330 t - x) \ m$. The frequency of the wave is: (in $Hz$)

Obtain the relation between wave velocity,angular frequency,and angular wave number.

For a wave equation given by $y = 2 \sin \pi (0.5x - 200t) \, cm$,what is the wave velocity in $cm/sec$?