When a wave propagating on a string gets reflected from a fixed rigid support,what is the change in its phase?

$A$ standing wave $y = A \sin \left( \frac{20}{3} \pi x \right) \cos (1000 \pi t)$ is maintained in a taut string,where $y$ and $x$ are expressed in meters. The distance between the successive points oscillating with the amplitude $A/2$ across a node is equal to ... $cm$.

$A$ standing wave having $3$ nodes and $2$ antinodes is formed between two atoms having a distance of $1.21 \; \mathring{A}$ between them. The wavelength of the standing wave is .... $\mathring{A}$

In stationary waves,all particles between two consecutive nodes pass through the mean position:

$A$ string is rigidly tied at two ends and its equation of vibration is given by $y = \sin(2\pi x) \cos(2\pi t)$. Then the minimum length of the string is .... $m$

Plane microwaves from a transmitter are directed normally towards a plane reflector. $A$ detector moves along the normal to the reflector. Between positions of $14$ successive maxima,the detector travels a distance of $0.13\, m$. If the velocity of light is $3 \times 10^8\, m/s$,find the frequency of the transmitter.