$A$ uniform string of length $L$ and mass $M$ is fixed at both ends while it is subject to a tension $T$. It can vibrate at frequencies $(v)$ given by the formula (where $n=1, 2, 3, \ldots$):

In a Sonometer experiment,the frequency of the tuning fork used is $288 \ Hz$. Harmonics will '$NOT$' be produced at the frequency: (in $Hz$)

$A$ stretched string of $1 \ m$ length and mass $5 \times 10^{-4} \ kg$ is having a tension of $20 \ N$. If it is plucked at $25 \ cm$ from one end,then it will vibrate with a frequency of ... $Hz$.

Two strings of the same material having lengths $L$ and $2L$,and radii $2r$ and $r$ respectively,are vibrating in the fundamental mode. The tension applied to both strings is the same. The ratio of their respective fundamental frequencies is:

$A$ steel wire of length $1 \,m$, mass $0.1 \,kg$, and uniform area of cross-section $10^{-6} \,m^2$ is rigidly fixed at both ends without any tension. Its temperature is lowered by $20^{\circ} C$ and transverse waves are set up by plucking the wire at the middle. The frequency of the fundamental mode is ($Y = 200 \,GPa$, $\alpha = 1.21 \times 10^{-5} {}^{\circ} C^{-1}$). (in $\,Hz$)

The length of a sonometer wire is $0.75\, m$ and density is $9 \times 10^3\, kg/m^3$. It can bear a stress of $8.1 \times 10^8\, N/m^2$ without exceeding the elastic limit. What is the fundamental frequency that can be produced in the wire in $Hz$?