To increase the frequency of transverse oscillations of a stretched string by $40\%$, the tension must be increased by (in $\%$)

$A$ stretched wire of length $110 \, cm$ is divided into three segments whose frequencies are in the ratio $1 : 2 : 3$. Their lengths must be:

$A$ wire of length $L$, diameter $d$, and density of material $\rho$ is under tension $T$ and has a fundamental frequency of vibration $n_A$. Another wire of length $2L$, diameter $3d$, and density of material $2\rho$ is vibrated under tension $2T$, and its fundamental frequency of vibration becomes $n_B$. The ratio $n_B : n_A$ is

The fundamental frequency of a sonometer wire is $n$. If the length and diameter of the wire are doubled while keeping the tension constant,what is the new fundamental frequency?

Two uniform stretched strings $A$ and $B$, made of steel, are vibrating 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 lengths of the strings is

Obtain the equation of frequency of oscillations in a string tied at both ends.