Two uniform strings $A$ and $B$ made of steel are made to vibrate under the same tension. If the first overtone of $A$ is equal to the second overtone of $B$ and if the radius of $A$ is twice that of $B$,the ratio of the length of string $B$ to that of $A$ is

Standing waves are generated on a sonometer string loaded with a cylindrical body. If the cylinder is completely immersed in water,the length of the loops changes by a factor of $2.2$. The specific gravity of the material of the cylinder is

$A$ string is under tension of $180 \ N$ and mass per unit length $2 \times 10^{-3} \ kg/m$. It produces two consecutive resonant frequencies with a tuning fork,which are $375 \ Hz$ and $450 \ Hz$. The mass of the string is: (in $g$)

When a sonometer wire vibrates in the third overtone, the number of antinodes and nodes formed on the wire are respectively

$A$ steel rod $100 \ cm$ long is clamped at its mid-point. The fundamental frequency of longitudinal vibrations of the rod is given to be $2.53 \ kHz$. What is the speed of sound in steel in $km/s$ (in $.06$)?

$A$ thin wire of length $99 \ cm$ is fixed at both ends as shown in the figure. The wire is kept under a tension and is divided into three segments of lengths $l_1, l_2$ and $l_3$ as shown in the figure. When the wire is made to vibrate, the segments vibrate respectively with their fundamental frequencies in the ratio $1: 2: 3$. Then, the lengths $l_1, l_2$ and $l_3$ of the segments respectively are (in $cm$):