$A$ uniform string is vibrating with a fundamental frequency '$n$'. If the radius and length of the string are both doubled while keeping the tension constant,then the new frequency of vibration 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

$A$ 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).

$A$ metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T$ ($Y =$ Young's modulus,$\rho =$ density,$\alpha =$ coefficient of linear expansion),then the frequency of transverse vibration is proportional to:

$A$ second harmonic has to be generated in a string of length $l$ stretched between two rigid supports. The points where the string has to be plucked and touched are

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