A steel rod of length $100\, cm$ is clamped at the middle. The frequency of the fundamental mode for the longitudinal vibrations of the rod is ..... $kHz$ (Speed of sound in steel $= 5\, km\, s^{-1}$)

A certain string will resonant to several frequencies, the lowest of which is $200 \,cps$. What are the next three higher frequencies to which it resonants?

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 ..... $Hz$

The length of a sonometer wire is $0.75\, m$ and density $9 \times 10^3\, kg/m^3$. It can bear a stress of $8.1 \times 10^8\, N/m^2$ without exceeding the elastic limit. What is the fundamental frequency that can be produced in the wire  .... $Hz$ ?

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 ........... $cps$

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