If ${n_1}, {n_2}, {n_3}, \dots$ are the frequencies of segments of a stretched string,the frequency $n$ of the string is given by

$A$ string on a musical instrument is $50 \ cm$ long and its fundamental frequency is $270 \ Hz$. If the desired frequency of $1000 \ Hz$ is to be produced,the required length of the string is .... $cm$.

$A$ 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 $\,cm$)

The fundamental frequency of a transverse wave of a stretched string subjected to a tension $T_1$ is $300 \ Hz$. If the length of the string is doubled and subjected to a tension of $T_2$, the fundamental frequency of the transverse wave in the string becomes $100 \ Hz$. Then $T_2: T_1=$ (Linear density of the string is constant)

The frequency of a sonometer wire is $n$. If its tension is increased $4$ times and its length is doubled,then the new frequency will be

$A$ wire of length $1 \,m$ under a certain initial tension emits a sound of fundamental frequency $256 \,Hz$. When the tension is increased by $1 \,kg \,wt$,the frequency of the fundamental note increases to $320 \,Hz$. The initial tension is ........... $kg \,wt$.