$A$ 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 remains the same. The frequency of the fork is ............. $Hz$.

$A$ sonometer wire $49 \ cm$ long is in unison with a tuning fork of frequency '$n$'. If the length of the wire is decreased by $1 \ cm$ and it is vibrated with the same tuning fork,$6$ beats are heard per second. The value of '$n$' is (in $Hz$)

$A$ string fixed at both ends is vibrating in two segments. The wavelength of the corresponding wave is

The fundamental frequency of a sonometer wire is $n$. If the tension is increased $3$ times,the length is increased $3$ times,and the diameter is increased $2$ times,what will be the new frequency?

$A$ wire of density $9 \times 10^3 \,kg/m^3$ is stretched between two clamps $1 \,m$ apart and is subjected to an extension of $4.9 \times 10^{-4} \,m$. What will be the lowest frequency of the transverse vibrations in the wire in $Hz$ $[Y = 9 \times 10^{10} \,N/m^2]$?

$A$ string in a musical instrument is $50 \,cm$ long and its fundamental frequency is $800 \,Hz$. Keeping the tension applied to the string same, the change in the length to produce a sound note of fundamental frequency $1000 \,Hz$ will be: (in $\,cm$)