In an experiment with a sonometer,a tuning fork of frequency $256 \ Hz$ resonates with a length of $25 \ cm$ and another tuning fork resonates with a length of $16 \ cm$. If the tension of the string remains constant,the frequency of the second tuning fork is .... $Hz$

$A$ stretched string is divided into three segments of lengths $50\,cm$,$40\,cm$,and $10\,cm$ with the help of bridges. Their vibrations will have frequencies in the ratio:

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 $kg$)

The tension of a stretched string is increased by $69\%$. In order to keep its frequency of vibration constant,its length must be increased by .... $\%$

$A$ metal wire of linear mass density of $9.8 \, g/m$ is stretched with a tension of $10 \, kg$ weight between two rigid supports $1 \, m$ apart. The wire passes at its middle point between the poles of a permanent magnet,and it vibrates in resonance when carrying an alternating current of frequency $n$. The frequency $n$ of the alternating source is ..... $Hz$.

$A$ uniform wire of length $L$,diameter $D$,and density $\rho$ is stretched by a tension $T$. The frequency $f$ of the wire is proportional to: