$A$ 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 $.06$)?

The fundamental frequency of a sonometer wire is $50 \ Hz$ 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?

$A$ sonometer wire has a length of $114 \ cm$, between two fixed ends. Where should two bridges be placed so as to divide the wire into three segments (in $cm$) whose fundamental frequencies are in the ratio $1:3:4$?

$A$ stretched string is vibrating in the second overtone. The number of nodes and antinodes between the ends of the string are respectively:

If the frequency of vibrations of a string is to be increased by a factor of two,then the tension in the string must be made:

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