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

When a string is divided into three segments of length $l_1,\,l_2$ and $l_3,$ the fundamental frequencies of these three segments are $v_1,\,v_2$ and $v_3$ respectively. The original fundamental frequency $(v)$ of the string is

Three sound waves of equal amplitudes have frequencies $(f-1 ), f, (f+ 1)$. They superpose to give beats. The number of beats produced per second will be:

The wave described by $y = 0.25\,\sin \,\left( {10\pi x - 2\pi t} \right)$ , where $x$ and $y$ are in $meters$ and $t$ in $seconds$ , is a wave travelling along is

The equation of transverse wave in stretched string is $y = 5\,\sin \,2\pi \left[ {\frac{t}{{0.04}} - \frac{x}{{50}}} \right]$ Where distances are in cm and time in second. The wavelength of wave is .... $cm$

The figure represents the instantaneous picture of a transverse harmonic wave traveling along the negative $x$-axis. Choose the correct alternative $(s)$ related to the movement of the nine points shown in the figure.  The stationary points is/are