What is the phase change of a wave when it reflects from a rigid support?

The equation of a transverse wave travelling on a rope is given by $y = 10\sin \pi (0.01x - 2.00t)$ where $y$ and $x$ are in $cm$ and $t$ is in $seconds$. The maximum transverse speed of a particle in the rope is about .... $cm/s$.

$A$ transverse wave travelling along a stretched string has a speed of $30 \ m/s$ and a frequency of $250 \ Hz$. The phase difference between two points on the string $10 \ cm$ apart at the same instant is

$A$ transverse wave is travelling along a stretched string from right to left. The figure shown represents the shape of the string at a given instant. At this instant,

The equation of a progressive wave is $y = 8 \sin \left[ \pi \left( \frac{t}{10} - \frac{x}{4} \right) + \frac{\pi}{3} \right]$. The wavelength of the wave is .... $m$.

The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t) = e^{-(ax^2 + bt^2 + 2\sqrt{ab}xt)}$. This represents: