$A$ wave $y = a \cos(kx - \omega t)$ superposes on another wave to form a stationary wave having a node at $x = 0$. What is the equation of the other wave?

$A$ 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?

$A$ stationary wave is formed with $3$ nodes along the length of a string of $90 \ cm$. The wavelength of the wave is: (in $cm$)

In a vibrating string with fixed ends,the waves are of type:

The pattern of standing waves formed on a stretched string at two instants of time (extreme,mean) are shown in the figure. The velocity of the two waves superimposing to form stationary waves is $360 \, ms^{-1}$ and their frequencies are $256 \, Hz$. Which is not a possible value of $t$ (in $\sec$)?

$A$ pulse of a wave train travels along a stretched string and reaches the fixed end of the string. It will be reflected back with