The length and diameter of a metal wire used in a sonometer are both doubled. The fundamental frequency will change from $n$ to:

In an experiment to study standing waves,you use a string whose mass per unit length is $\mu = (1.0 \pm 0.1) \times 10^{-4} \ kg/m$. You look at the fundamental mode,whose frequency $f$ is related to the length $L$ and tension $T$ of the string by the equation $L = \frac{1}{2f} \sqrt{\frac{T}{\mu}}$. You make a plot with $L$ on the $y$-axis and $\sqrt{T}$ on the $x$-axis,and find that the best-fitting line is $y = (8.0 \pm 0.3) \times 10^{-3}x + (0.2 \pm 0.04)$ in $SI$ units. What is the value of the frequency of the wave (including the error)? Express your result in $SI$ units $(Hz)$.

Two wires are fixed in a sonometer. Their tensions are in the ratio $8:1$. The lengths are in the ratio $36:35$. The diameters are in the ratio $4:1$. Densities of the materials are in the ratio $1:2$. If the lower frequency in the setting is $360 \ Hz$,the beat frequency when the two wires are sounded together is: (in $Hz$)

$A$ 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 $kg$)

In a sonometer experiment, the fundamental frequency of vibration of a wire is '$n_1$' when the wire is stretched by hanging a metal bob. If the bob is completely immersed in water, the frequency of vibration of the wire becomes '$n_2$'. The relative density of the metal of the bob is

The frequency of a sonometer wire is $f$. When the weights producing the tension are completely immersed in water,the frequency becomes $f/2$. When the weights are immersed in a certain liquid,the frequency becomes $f/3$. The specific gravity of the liquid is: