$A$ string is under tension of $180 \ N$ and mass per unit length $2 \times 10^{-3} \ kg/m$. It produces two consecutive resonant frequencies with a tuning fork,which are $375 \ Hz$ and $450 \ Hz$. The mass of the string is: (in $g$)

At poles,a stretched wire of a given length vibrates in unison with a tuning fork. At the equator,for the same setting,to produce resonance with the same fork,the vibrating length of the wire

If you set up the ninth harmonic on a string fixed at both ends,its frequency compared to the seventh harmonic is:

$A$ sonometer wire has a length of $114 \ cm$, between two fixed ends. Where should two bridges be placed so as to divide the wire into three segments (in $cm$) whose fundamental frequencies are in the ratio $1:3:4$?

Two similar sonometer wires have fundamental frequencies of $500 \, Hz$. They are under the same tension. By what percentage should the tension be increased in one wire so that the two wires produce $5 \, \text{beats/sec}$ (in $\%$)?

$A$ sonometer wire resonates with $4$ antinodes between two bridges for a given tuning fork, when $1 \,kg$ mass is suspended from the wire. Using the same fork, when mass $M$ is suspended, the wire resonates producing $2$ antinodes between the two bridges (the distance between the two bridges remains the same). The value of $M$ is: (in $\,kg$)