Two identical piano wires, kept under the same tension $T$ have a fundamental frequency of $600\, Hz$. The fractional increase in the tension of one of the wires which will lead to occurrence of $6\, beats/s$ when both the wires oscillate together would be

A transverse wave in a medium is described by the equation $y = A \sin^2 \,(\omega t -kx)$. The magnitude of the maximum velocity of particles in the medium will be equal to  that of the wave velocity, if the value of $A$ is ($\lambda$ = wavelngth of wave)

Two vibrating strings of the same material but lengths $L$ and $2L$ have radii $2r$ and $r$ respectively. They are stretched under the same tension . Both the strings vibrate in their fundamental modes, the one of length $L$ with frequency $f_1$ and the other with frequency $f_2$. The ratio $\frac{f_1}{f_2}$ 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 ..... $m$

Two identical flutes produce fundamental notes of frequency $300\,Hz$ at $27\,^oC$. If the temperature of air in one flute is increased to $31\,^oC$, the number of the beats heard per second will be

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 ..... $unit$