A cylindrical tube $(L = 120\, cm.)$ is resonant with a tuning fork of frequency $330\, Hz$. If it is filling by water then to get resonance again, minimum length of water column is  …… $cm$  $(v_{air} = 330\, m/s)$

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)

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

A wave travelling along the $x- $ axis is described by the equation $y(x, t) = 0.005\,\,cos(\alpha x\,-\,\beta t).$  If the wavelength and the time period of the wave are $0.08 \,\,m$ and $2.0\,\,s,$  respectively, then $\alpha $ and $\beta $ in appropriate units are

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