The tension in a piano wire is $10N$. What should be the tension in the wire to produce a note of double the frequency …. $N$

A string is stretched between fixed points separated by $75.0\ cm$. It is observed to have resonant frequencies of $420\ Hz$ and $315\ Hz.$ There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is  …. $Hz$

A string is stretched so that its length is increased by $\frac{1}{\eta }$ of its original length. The ratio of fundamental frequency of transverse vibration to that of fundamental frequency of longitudinal vibration will be

Two identical strings $X$ and $Z$ made of same material have tension $T _{ x }$ and $T _{ z }$ in them. If their fundamental frequencies are $450\, Hz$ and $300\, Hz ,$ respectively, then the ratio $T _{ x } / T _{ z }$ is$…..$

The fundamental frequency of vibration of a string stretched between two rigid support is $50\,Hz$. The mass of the string is $18\,g$ and its linear mass density is $20\,g / m$. The speed of the transverse waves so produced in the string is $……….\,ms ^{-1}$