$n$ waves are produced on a string in $1 \ s$. When the radius of the string is doubled,keeping the tension the same,the number of waves produced in $1 \ s$ for the same harmonic will be

Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the $2^{\text{nd}}$ overtone of the $2^{\text{nd}}$ wire and the radius of the first wire is twice the radius of the $2^{\text{nd}}$ wire,then the ratio of the length of the first wire to the $2^{\text{nd}}$ wire is:

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

When a string of length $l$ is divided into three segments of length $l_1, l_2$ and $l_3$,the fundamental frequencies of the three segments are $n_1, n_2$ and $n_3$ respectively. The original fundamental frequency $n$ of the string is:

When a stretched wire of fundamental frequency $f$ is divided into three segments,the fundamental frequencies of these three segments are $f_1, f_2$ and $f_3$ respectively. Then the relation among $f_1, f_2, f_3$ and $f$ is (Assume tension is constant).

$A$ string of length $1 \,m$ and mass $2 \times 10^{-5} \,kg$ is under tension $T$. When the string vibrates, two successive harmonics are found to occur at frequencies $750 \,Hz$ and $1000 \,Hz$. The value of tension $T$ is . . . . . . Newton.