Two wires are producing fundamental notes of the same frequency. Change in which of the following factors of one wire will not produce beats between them

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 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

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 frequency of a sonometer wire is $f$, but when the weights producing the tensions are completely immersed in water the frequency becomes $f/2$ and on immersing the weights in a certain liquid the frequency becomes $f/3$. The specific gravity of the liquid is: 

A pipe closed at one end produces a fundamental note of $412\,Hz.$  It is cut into two pieces of equal length the fundamental notes produced by the two pieces are