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

The displacement of an elastic wave is given by the function : $y = 3\, sin\,\omega t + 4\, cos\,\omega t$ where $y$ is in $cm$ and $t$ is in $s$. The resultant amplitude is ...... $cm$

A point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$are at distances of $2m$ and $3m$ respectively from the source. The ratio of the intensities of the waves at $P$ and $Q$ is

If $n_1 , n_2$ and $n_3$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by

For a certain organ pipe three successive resonance frequencies are observed at $425\, Hz,$ $595\,Hz$ and $765\,Hz$ respectively. If the speed of sound in air is $340\,m/s,$ then the length of the pipe is ..... $m$

A wave $y = a\,\sin \,\left( {\omega t - kx} \right)$ on a string meets with another wave producing a node at $x = 0$. Then the equation of the unknown wave is