$A$ tuning fork gives $4$ beats with $50 \ cm$ length of a sonometer wire. If the length of the wire is shortened by $1 \ cm$,the number of beats is still the same. The frequency of the fork is (in $Hz$)

The fundamental frequency of a sonometer wire is $50 \ Hz$ for a given length and tension. If the length is increased by $25 \%$ while keeping the tension constant,what is the percentage change in the frequency of the second harmonic?

$A$ device used for investigating the vibration of a fixed string or wire is

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

$A$ 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 correct graph between the frequency $n$ and the square root of density $(\rho)$ of a wire,keeping its length,radius,and tension constant,is: