The equation of a stationary wave on a string clamped at both ends and vibrating in the third harmonic is $Y = 0.5 \sin(0.314 x) \cos(600 \pi t)$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. The length of the vibrating string is: (in $cm$)

The pattern of standing waves formed on a stretched string at two instants of time is shown in the figure. The velocity of the two waves superimposing to form stationary waves is $360 \ m/s$ and their frequencies are $256 \ Hz$.
$(a)$ Calculate the time at which the second curve is plotted.
$(b)$ Mark nodes and antinodes on the curve.
$(c)$ Calculate the distance between $A^{\prime}$ and $C^{\prime}$.

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

$A$ string fixed at both its ends vibrates in $5$ loops as shown in the figure. The total number of nodes and antinodes are respectively:

Explain the reflection of a wave at a rigid support.

The phase difference between the two particles situated on both the sides of a node in a stationary wave is ... $^o$.