The equation of a stationary wave is $y = 10 \sin \left( \frac{\pi x}{4} \right) \cos (20 \pi t)$. The distance between two consecutive nodes is:

Two progressive waves are travelling towards each other with velocity $50 \,m/s$ and frequency $200 \,Hz$. The distance between two consecutive antinodes is (in $\,m$)

$A$ 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 following statements are given for a stationary wave:
$(a)$ Every particle has a fixed amplitude which is different from the amplitude of its nearest particle.
$(b)$ All the particles cross their mean position at the same time.
$(c)$ All the particles are oscillating with the same amplitude.
$(d)$ There is no net transfer of energy across any plane.
$(e)$ There are some particles which are always at rest.
Which of the following is correct?

$A$ progressive wave travelling in the positive $x$-direction is given by $y = a \sin(kx - \omega t)$. It meets a fixed end at $x = 0$. The reflected wave may be given by:

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