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:

The first overtone of a stretched wire of given length is $320 \ Hz$. The first harmonic is .... $Hz$.

The length of the string of a musical instrument is $90 \;cm$ and has a fundamental frequency of $120 \;Hz$. Where (in $cm$) should it be pressed to produce a fundamental frequency of $180 \;Hz$?

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

$A$ stretched string of $1 \ m$ length and mass $5 \times 10^{-4} \ kg$ is having a tension of $20 \ N$. If it is plucked at $25 \ cm$ from one end,then it will vibrate with a frequency of ... $Hz$.

$A$ sonometer wire resonates with $4$ antinodes between two bridges for a given tuning fork, when $1 \,kg$ mass is suspended from the wire. Using the same fork, when mass $M$ is suspended, the wire resonates producing $2$ antinodes between the two bridges (the distance between the two bridges remains the same). The value of $M$ is: (in $\,kg$)