A tuning fork and a sonometer wire were sounded together and produce $4$ beats per second. When the length of sonometer wire is $95 cm$ or $100 cm,$ the frequency of the tuning fork is ..... $Hz$

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 $...... {m}$

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

The length, tension, diameter and density of a wire $B$ are double than the corresponding quantities for another stretched wire $A$. Then.

A tuning fork gives $4$ beats with $50\, cm$ length of a sonometer wire if the length of  the wire is shortened by $1\, cm$. the no. of beats still the same. The frequency of the  fork is -............. $\mathrm{Hz}$

A string in musical instrument is $50 cm$ long and its fundamental frequency is $800 Hz.$ If a frequency of $1000 Hz$ is to be produced, then required length of string is ..... $cm$