$A$ sonometer wire '$A$' of diameter '$d$' under tension '$T$' having density '$\rho_1$' vibrates with fundamental frequency '$n$'. If we use another wire '$B$' which vibrates with the same frequency under tension '$2T$' and diameter '$2d$',then the density '$\rho_2$' of wire '$B$' will be:

Three similar wires of frequencies $n_1, n_2$ and $n_3$ are joined to form a single wire. What will be its resulting frequency $n$?

Two uniform wires of the same material are vibrating under the same tension. If the first overtone of the first wire is equal to the second overtone of the second wire and the radius of the first wire is twice the radius of the second wire,then the ratio of the lengths of the first wire to the second wire is:

$A$ second harmonic has to be generated in a string of length $l$ stretched between two rigid supports. The points where the string has to be plucked and touched are respectively

Show that when a string fixed at its two ends vibrates in $1$ loop,$2$ loops,$3$ loops and $4$ loops,the frequencies are in the ratio $1 : 2 : 3 : 4$.

An iron load of $2 \ kg$ is suspended in air from the free end of a sonometer wire of length $1 \ m$. $A$ tuning fork of frequency $256 \ Hz$ is in resonance with $\frac{1}{\sqrt{7}}$ times the length of the sonometer wire. If the load is immersed in water, the length of the wire in metres that will be in resonance with the same tuning fork is (Specific gravity of iron $= 8$).