The tension in a wire is decreased by $19 \%$. The percentage decrease in frequency will be ......... $\%$

If $n _{1}, n_{2}$ and $n _{3}$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by

A tuning fork of frequency $480 Hz$ produces $10$ beats per second when sounded with a vibrating sonometer string. What must have been the frequency of the string if a slight increase in tension produces lesser beats per second than before ..... $Hz$

Calculate the frequency of the second harmonic formed on a string of length $0.5 m$ and mass $2 × 10^{-4}$ kg when stretched with a tension of $20 N$ .... $Hz$

A wire having a linear mass density $9.0 \times 10^{-4} \;{kg} / {m}$ is stretched between two rigid supports with a tension of $900\; {N}$. The wire resonates at a frequency of $500\;{Hz}$. The next higher frequency at which the same wire resonates is $550\; {Hz}$. The length of the wire is $...... {m}$

A string on a musical instrument is $50 cm$ long and its fundamental frequency is $270 Hz$. If the desired frequency of $1000 Hz$ is to be produced, the required length of the string is .... $cm$