$A$ uniform wire of length $L$,diameter $D$,and density $\rho$ is stretched by a tension $T$. The frequency $f$ of the wire is proportional to:

Two strings $A$ and $B$ of lengths $L_A = 80 \text{ cm}$ and $L_B = x \text{ cm}$ respectively are used separately in a sonometer. The ratio of their densities $(d_A / d_B)$ is $0.81$. The diameter of $B$ is one-half that of $A$. If the strings have the same tension and fundamental frequency, the value of $x$ is:

The first overtone of a stretched wire of given length is $320 \ Hz$. The first harmonic is .... $Hz$.

$A$ stretched string is vibrating in the second overtone. The number of nodes and antinodes between the ends of the string are respectively:

Two similar sonometer wires have fundamental frequencies of $500 \, Hz$. They are under the same tension. By what percentage should the tension be increased in one wire so that the two wires produce $5 \, \text{beats/sec}$ (in $\%$)?

The fundamental frequency of a sonometer wire increases by $6\, Hz$ if its tension is increased by $44\%$,keeping the length constant. The frequency of the wire is ...... $Hz$.