A vibrating string of certain length $l$ under a tension $T$ resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75\, cm$ inside a tube closed at one end. The string also generates $4\, beats$ per second when excited along with a tuning fork of frequency $n$. Now when the tension of the string is slightly increased the number of beats reduces to $2\, per second$. Assuming the velocity of sound in air to be $340\, m/s$, the frequency $n$ of the tuning fork in $Hz$ is

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

Unlike a laboratory sonometer, a stringed instrument is seldom plucked in the middle. Supposing a sitar string is plucked at about $\frac{1}{4}$th of its length from the end. The most prominent harmonic would be

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

The length of a son meter wire $AB$ is $110\; cm$. Where should the two bridges be placed from $A$ to divide the wire in $3$ segments whose fundamental frequencies are in the ratio of $1:2:3$?