The fundamental frequency of a sonometer wire is $n$. If the length and diameter of the wire are doubled while keeping the tension constant,what is the new fundamental frequency?

Two uniform wires of same material are vibrating under the same tension. If the $1^{\text{st}}$ overtone of the $1^{\text{st}}$ wire is equal to the $2^{\text{nd}}$ overtone of the $2^{\text{nd}}$ wire and the radius of the $1^{\text{st}}$ wire is twice the radius of the $2^{\text{nd}}$ wire,find the ratio of the length of the $1^{\text{st}}$ wire to that of the $2^{\text{nd}}$ wire.

The fundamental frequency of a sonometer wire is $50 \text{ Hz}$ for a given length and tension. If the length is increased by $25\%$ while keeping the tension constant, what is the percentage change in the frequency of the second harmonic?

$A$ wire of length $0.3\,m$,stretched between rigid supports,has its $n^{\text{th}}$ and $(n+1)^{\text{th}}$ harmonics at $400\,Hz$ and $450\,Hz$,respectively. If the tension in the string is $2700\,N$,its linear mass density is ......... $kg/m$.

When tension $T$ is applied to a sonometer wire of length $\ell$,it vibrates with the fundamental frequency $n$. Keeping the experimental setup same,when the tension is increased by $8 \ N$,the fundamental frequency becomes three times the earlier fundamental frequency $(n)$. The initial tension applied to the wire in newton was:

Two strings of the same material having lengths $L$ and $2L$,and radii $2r$ and $r$ respectively,are vibrating in the fundamental mode. The tension applied to both strings is the same. The ratio of their respective fundamental frequencies is: