The stationary wave $y = 2a{\mkern 1mu} \,\,sin\,\,{\mkern 1mu} kx{\mkern 1mu} \,\,cos{\mkern 1mu} \,\omega t$ in a stretched string is the result of superposition of $y_1 = a\,sin\,(kx -\omega t)$ and

A stretched string is divided into three segments of lengths $50\,cm,\,\,40\,cm$ and $10\,cm$ with the help of bridges. Their vibrations will have frequencies in the ratio

The phase difference corresponding to path difference of $x$ is

A transverse harmonic wave on a string is described by $y = 3\sin \left( {36t + 0.018x + \frac{\pi }{4}} \right)$ where $x$ and $y$ are in $cm$ and $t$ in $s$. The least distance between two successive crests in the wave is .... $m$

A closed organ pipe has length $L$ , the air in it is vibrating in third overtone with maximum amplitude $'a'$ . The amplitude at distance $\frac {L}{7}$ from closed end of the pipe is

Two waves represented by ${y_1} = a\sin \frac{{2\pi}}{\lambda }\left( {vt - x} \right)$ and ${y_2} = a\cos \frac{{2\pi }}{\lambda }\left( {vt - x} \right)$ are superposed. The resultant wave has an amplitude equal to