Two uniform wires of 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 length of the first wire to the second wire is:

$A$ string in a musical instrument is $50 \ cm$ long and its fundamental frequency is $800 \ Hz$. If a frequency of $1000 \ Hz$ is to be produced,then the required length of the string is ..... $cm$.

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 $= 8$).

In a sonometer experiment,a string of length $L$ under tension vibrates in its second overtone between two bridges. The amplitude of vibration is maximum at:

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:

$A$ piano string $1.5 \, m$ long is made of steel of density $7.7 \times 10^3 \, kg/m^3$ and Young's modulus $2 \times 10^{11} \, N/m^2$. It is maintained at a tension which produces an elastic strain of $1 \%$ in the string. The fundamental frequency of transverse vibrations of the string is ......... $Hz$.