When a sonometer wire vibrates in the third overtone,there are:

$A$ sonometer wire resonates with $4$ antinodes between the two bridges for a given tuning fork when a $1 \text{ kg}$ 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 bridges remains the same). The value of $M$ is: (in $\text{ kg}$)

$A$ 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 ... $Hz$.

The fundamental frequency of a sonometer wire increases by $9 \ Hz$,if its tension is increased by $69 \%$,keeping the length constant. The frequency of the wire is (in $Hz$)

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 $\%$)?

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