$A$ wire of length $2L$ 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

Two uniform strings $A$ and $B$ made of steel are made to vibrate 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 length of string $B$ to that of $A$ is

$A$ metal wire of linear mass density of $9.8 \, g/m$ is stretched with a tension of $10 \, kg$ weight between two rigid supports $1 \, m$ apart. The wire passes at its middle point between the poles of a permanent magnet,and it vibrates in resonance when carrying an alternating current of frequency $n$. The frequency $n$ of the alternating source is ..... $Hz$.

The frequency of transverse vibrations in a stretched string is $200 \ Hz$. If the tension is increased four times and the length is reduced to one-fourth the original value,the frequency of vibration will be .... $Hz$.

$A$ sonometer wire is vibrating in the third overtone. There are:

$A$ string fixed at both ends vibrates in three loops. The wavelength is $10 \, cm$. The length of the string is .... $cm$.