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

To increase the frequency from $100 Hz$ to $400 Hz$ the tension in the string has to be changed by ….. $times$

A wave is reflected from a rigid support. The change in phase on reflection will be

A uniform metal wire of density $\rho $, cross-sectional area $A$ and length $L$ is stretched with a tension $T$. The speed of transverse wave in the wire is given by

The string of a violin has a frequency of $440 \,cps$. If the violin string is shortened by one fifth, its frequency will be changed to ……….. $cps$