A wire of length $30\,cm$, stretched between rigid supports, has it's $n^{\text {th}}$ and $(n+1)^{\text {th}}$ harmonics at $400\,Hz$ and $450\; Hz$, respectively. If tension in the string is $2700\,N$, it's linear mass density is.........$kg/m$.

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 .... $cm$

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

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

The string of a violin has a frequency of $440 \,cps$. If the violin string is shortened by one fifth, its frequency will be changed to ........... $cps$