$A$ wire of density $9 \times 10^{-3} \,kg\, cm^{-3}$ is stretched between two clamps $1 \,m$ apart. The resulting strain in the wire is $4.9 \times 10^{-4}$. The lowest frequency of the transverse vibrations in the wire is......$Hz$ (Young's modulus of wire $Y = 9 \times 10^{10} \,N m^{-2}$),(to the nearest integer).

$A$ stone is hung in air from a wire which is stretched over a sonometer. The bridges of the sonometer are $L \, cm$ apart when the wire is in unison with a tuning fork of frequency $N$. When the stone is completely immersed in water,the length between the bridges is $l \, cm$ for re-establishing unison. The specific gravity of the material of the stone is:

If ${n_1}, {n_2}, {n_3}, \dots$ are the frequencies of segments of a stretched string,the frequency $n$ of the string is given by

Two tuning forks when sounded together produce $4$ beats per second. One of the forks is in unison with $23 \ cm$ length of a sonometer wire and the other with $24 \ cm$ length of the same wire. The frequencies of the two tuning forks are

The fundamental frequency of a sonometer with a weight of $4\,kg$ is $256\,Hz$. The weight required to produce its octave is .... $kg-wt$

$A$ 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.