The figure shows a stationary wave between two fixed points $P$ and $Q$. Which point$(s)$ among $1, 2,$ and $3$ are in phase with point $X$?

$A$ wave disturbance in a medium is described by $y(x, t) = 0.02 \cos(50 \pi t + \frac{\pi}{2}) \cos(10 \pi x)$, where $x$ and $y$ are in meters and $t$ is in seconds. Which statement$(s)$ is/are correct?

$A$ 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:

The distance between the nearest node and antinode in a stationary wave is

$A$ string is vibrating in its fifth overtone between two rigid supports $2.4 \ m$ apart. The distance between successive node and antinode is (in $m$)

$A$ standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by $y(x, t) = 0.5 \sin(\frac{5\pi}{4}x) \cos(200\pi t)$. What is the speed of the travelling wave moving in the positive $x$ direction in $m/s$? ($x$ and $t$ are in meter and second,respectively.)