If the tension of a sonometer wire increases four times,then the fundamental frequency of the wire will increase by how many times?

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 $180 \;Hz$?

$A$ string vibrates in its fundamental mode when a tension $T_1$ is applied to it. If the length of the string is decreased by $25 \%$ and the tension applied is changed to $T_2$, the fundamental frequency of the string increases by $100 \%$, then $\frac{T_2}{T_1} =$ (Linear density of the string is constant)

The fundamental frequency of a sonometer wire is $n$. If the length,tension,and diameter of the wire are all tripled,what is the new fundamental frequency?

Unlike a laboratory sonometer,a stringed instrument is seldom plucked in the middle. Supposing a sitar string is plucked at about $\frac{1}{4}$th of its length from the end. The most prominent harmonic would be

The total length of a sonometer wire between fixed ends is $110 \ cm$. Two bridges are placed to divide the length of the wire in the ratio $6 : 3 : 2$. The tension in the wire is $400 \ N$ and the mass per unit length is $0.01 \ kg/m$. What is the minimum common frequency with which the three parts can vibrate in $Hz$?