$A$ 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:

Write the equation of a stationary wave and obtain the equations of nodes and antinodes by defining them.

$A$ standing wave exists in a string of length $150 \ cm$,which is fixed at both ends with rigid supports. The displacement amplitude of a point at a distance of $10 \ cm$ from one of the ends is $5\sqrt{3} \ mm$. The nearest distance between two points,within the same loop and having a displacement amplitude equal to $5\sqrt{3} \ mm$,is $10 \ cm$. Find the maximum displacement amplitude of the particles in the string (in $mm$).

$A$ 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 metres and $t$ is in seconds.

$A$ stretched string is fixed at both ends. It is made to vibrate so that the total number of nodes formed in it is '$x$'. The length of the string in terms of the wavelength of waves formed in it is $(\lambda = \text{wavelength})$

Which property distinguishes between progressive and stationary waves?