$A$ string of length $1 \, m$ fixed at both ends is vibrating in the $3^{rd}$ overtone. The tension in the string is $200 \, N$ and the linear mass density is $5 \, g/m$. The frequency of these vibrations is ..... $Hz$.

If the length of a stretched string is reduced by $40 \%$ and the tension is increased by $44 \%$,then the ratio of the final to the initial frequencies of the stretched string is:

$A$ segment of wire vibrates with a fundamental frequency of $450 \,Hz$ under a tension of $9 \,kg-wt$. The tension at which the fundamental frequency of the same wire becomes $900 \,Hz$ is:

In an experiment with a sonometer,a tuning fork of frequency $256 \ Hz$ resonates with a length of $25 \ cm$ and another tuning fork resonates with a length of $16 \ cm$. If the tension of the string remains constant,the frequency of the second tuning fork is .... $Hz$

Two uniform wires of same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and the radius of the first wire is twice the radius of the second wire, then the ratio of the length of the first wire to the second wire is:

If you set up the ninth harmonic on a string fixed at both ends,its frequency compared to the seventh harmonic is: