$A$ string vibrates according to the equation $y = 5 \sin \left( \frac{2\pi x}{3} \right) \cos (20\pi t)$,where $x$ and $y$ are in $cm$ and $t$ is in $sec$. The distance between two adjacent nodes is .... $cm$.

From the given progressive wave equations,which waves are used to produce a standing wave?
$z_1 = A \cos(\omega t - kx)$
$z_2 = A \cos(\omega t + kx)$
$z_3 = A \cos(\omega t + ky)$
$z_4 = A \cos(2\omega t - 2ky)$

In a stationary wave,all the particles:

$A$ stationary wave is represented by $y = 10 \sin \left( \frac{\pi x}{4} \right) \cos (20 \pi t)$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. The distance between two consecutive nodes is (in $cm$)

The following equations represent progressive transverse waves:
$Z_1 = A \cos(\omega t - kx)$,
$Z_2 = A \cos(\omega t + kx)$,
$Z_3 = A \cos(\omega t + ky)$,
$Z_4 = A \cos(2\omega t - 2ky)$.
$A$ stationary wave will be formed by superposing:

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 $X$?