The tension of a stretched string is increased by $69\%$. In order to keep its frequency of vibration constant,its length must be increased by .... $\%$

When a vibrating tuning fork is placed on a sound box of a sonometer,$8$ beats per second are heard when the length of the sonometer wire is kept at $101 \,cm$ or $100 \,cm$. Then the frequency of the tuning fork is (Consider that the tension in the wire is kept constant). (in $\,Hz$)

The fundamental frequency of a sonometer wire is $n$. If its radius is doubled and its tension becomes half,while the material of the wire remains the same,the new fundamental frequency will be

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:

Two identical strings of length $\ell$ and $2\ell$ vibrate with fundamental frequencies $N$ Hz and $1.5N$ Hz,respectively. The ratio of tensions for the smaller length to the larger length is

$A$ string fixed at both ends vibrates in three loops. The wavelength is $10 \, cm$. The length of the string is .... $cm$.