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

The fundamental frequency of a sonometer wire increases by $6$ $Hz$ if its tension is increased by $44\%$ keeping the length constant. The change in the fundamental frequency of the sonometer wire in $Hz$ when the length of the wire is increased by $20\%$, keeping the original tension in the wire will be :-

A wire of length $L$ and mass per unit length $6.0\times 10^{-3}\; \mathrm{kgm}^{-1}$ is put under tension of $540\; \mathrm{N}$. Two consecutive frequencies that it resonates at are : $420\; \mathrm{Hz}$ and $490 \;\mathrm{Hz}$. Then $\mathrm{L}$ in meters is

A wire of length $2\,L$ is made by joining two wires $A$ and $B$ of same lengths but different radii $r$ and $2r$ and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire $A$ is $p$ and that in $B$ is $q$ then the ratio $p : q$ is

A transverse wave is travelling along a stretched string from right to left. The figure  shown represents the shape of the string at a given instant. At this instant

Two identical strings $X$ and $Z$ made of same material have tension $T _{ x }$ and $T _{ z }$ in them. If their fundamental frequencies are $450\, Hz$ and $300\, Hz ,$ respectively, then the ratio $T _{ x } / T _{ z }$ is$.....$