$A$ tuning fork gives $4$ beats with $50 \ cm$ length of a sonometer wire. If the length of the wire is shortened by $1 \ cm$,the number of beats is still the same. The frequency of the fork is (in $Hz$)

In a sonometer experiment,a string of length $L$ under tension vibrates in its second overtone between two bridges. The amplitude of vibration is maximum at:

If we add $3 \ kg$ load to the hanger of a sonometer,the fundamental frequency becomes two times its initial value. The initial load must be (in $kg$)

$A$ sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $9 \ kg$ is suspended from the wire. When this mass is replaced by a mass $M$,the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of $M$ is ... $kg$.

$n$ waves are produced on a string in $1 \ s$. When the radius of the string is doubled,keeping the tension the same,the number of waves produced in $1 \ s$ for the same harmonic will be

$A$ stretched wire of length $260 \ cm$ is set into vibrations. It is divided into three segments whose frequencies are in the ratio $2:3:4$. Their lengths must be