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

$A$ wave represented by the equation $y = a \cos (kx - \omega t)$ is superposed with another wave to form a stationary wave such that the point $x = 0$ is a node. The equation for the other wave is:

Two waves are approaching each other with a velocity of $20 \ m/s$ and frequency $n$. The distance between two consecutive nodes is

$(i)$ For the wave $y(x, t) = 0.06 \sin \left(\frac{2 \pi}{3} x\right) \cos (120 \pi t)$,where $x$ and $y$ are in $m$ and $t$ is in $s$. The length of the string is $1.5 \, m$ and its mass is $3.0 \times 10^{-2} \, kg$. Do all the points on the string oscillate with the same $(a)$ frequency,$(b)$ phase,$(c)$ amplitude? Explain your answers.
$(ii)$ What is the amplitude of a point $0.375 \, m$ away from one end?

Standing stationary waves can be obtained in an air column even if the interfering waves are

In stationary waves,the distance between a node and its nearest antinode is $20 \ cm$. The phase difference between two particles having a separation of $60 \ cm$ will be