A vibrating string of certain length $\ell$ under a tension $\mathrm{T}$ resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75 \mathrm{~cm}$ inside a tube closed at one end. The string also generates $4$ beats per second when excited along with a tuning fork of frequency $\mathrm{n}$. Now when the tension of the string is slightly increased the number of beats reduces $2$ per second. Assuming the velocity of sound in air to be $340 \mathrm{~m} / \mathrm{s}$, the frequency $\mathrm{n}$ of the tuning fork in $\mathrm{Hz}$ is

Stationary waves are produced in $10\,m$  long stretched string. If the string Vibrates in $5$ segments and wave velocity  $20\,m/s$ the frequency is ..... $Hz$

A rod of length $1.2\,m$ is clamped at the mid point and its fundamental frequency is $2\,MHz$ , then speed of wave inside the rod?

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 .... $\%$

A tuning fork vibrating with a sonometer having $20 cm$ wire produces $5$ beats per second. The beat frequency does not change if the length of the wire is changed to $21 cm.$ the frequency of the tuning fork (in Hertz) must be

A sonometer wire, with a suspended mass of $M = 1\, kg$, is in resonance with a given tuning fork. The apparatus is taken to the moon where the acceleration due to gravity is $(1/6)$ that on earth. To obtain resonance on the moon, the value of $M$ should be ......... $kg$