Two waves represented by

$y_1 = 10\,sin\,(2000\,\pi t + 2x)$

and ${y_2} = 10{\mkern 1mu} \,sin\,{\mkern 1mu} \left( {2000{\mkern 1mu} \pi t + 2x + \frac{\pi }{2}} \right)$ are superposed at any point at a particular instant. The resultant amplitude is ..... $unit$

Two open organ pipes of fundamental frequencies $n_1$ and $n_2$ are joined in series.  The fundamental frequency of the new pipe so obtained will be

A transverse wave is described by the equation $y = {y_0}\,\sin \,2\pi \left( {ft - \frac{x}{\lambda }} \right)$ . The maximum particle velocity is equal to four times the wave velocity if

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

A string with a mass density of $4\times10^{-3}\, kg/m$ is under tension of $360\, N$ and is fixed at both ends. One of its resonance frequencies is $375\, Hz$. The next higher resonance frequency is $450\, Hz$. The mass of the string is

In the standing wave shown, particles at the positions $A$ and $B$ have a phase difference of