$A$ body is suspended from a string of length $1 \ m$ and mass $2 \ g$. The mass of the body required to produce a fundamental mode of $100 \ Hz$ frequency in the string is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)

The fundamental frequency of a sonometer wire of length $l$ is $n_0$. $A$ bridge is now introduced at a distance of $\Delta l$ (where $\Delta l \ll l$) from the center of the wire. The lengths of wire on the two sides of the bridge are now vibrated in their fundamental modes. Then,the beat frequency is nearly

At the poles,a stretched wire of a given length vibrates in unison with a tuning fork. At the equator,for the same setting to produce resonance with the same fork,the vibrating length of the wire

$A$ sonometer wire resonates with a given tuning fork,forming a standing wave with $5$ antinodes between two bridges when a mass of $9 \ kg$ is suspended from the wire. When a mass '$m$' is suspended from the wire,with the same tuning fork and the same length between the two bridges,$3$ antinodes are formed. The value of mass '$m$' is: (in $kg$)

$A$ string is stretched between two rigid supports separated by $75 \,cm$. There are no resonant frequencies between $420 \,Hz$ and $315 \,Hz$. The lowest resonant frequency for the string is (in $\,Hz$)

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?