If the length of a stretched string is shortened by $40\%$ and the tension is increased by $44\%$,then the ratio of the final and initial fundamental frequencies is

In a sonometer experiment,a string of length $L$ under tension vibrates in its second overtone between two bridges. The amplitude of vibration is maximum at:

$A$ steel rod $100 \ cm$ long is clamped at its mid-point. The fundamental frequency of longitudinal vibrations of the rod is given to be $2.53 \ kHz$. What is the speed of sound in steel in $km/s$ (in $.06$)?

$A$ 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 $\,kg$)

In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to $\frac{3}{4}$ of the original length and the tension is changed. The factor by which the tension is to be changed is

The frequency of the first harmonic of a string stretched between two points is $100 \, Hz$. The frequency of the third overtone is ... $Hz$.