To increase the frequency of transverse oscillations of a stretched string by $40\%$, the tension must be increased by (in $\%$)

If the tension and diameter of a sonometer wire of fundamental frequency $n$ are doubled and density is halved,then its fundamental frequency will become

Three similar wires of frequencies $n_1, n_2$ and $n_3$ are joined to form a single wire. What will be its resulting frequency $n$?

$A$ tuning fork is sounded with a sonometer wire of length $95 \, cm$ or $100 \, cm$,producing $4$ beats per second in both cases. What is the frequency of the tuning fork in $Hz$?

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 lengths of the strings is :

Two tuning forks when sounded together produce $4$ beats per second. One of the forks is in unison with $23 \ cm$ length of a sonometer wire and the other with $24 \ cm$ length of the same wire. The frequencies of the two tuning forks are