A string is producing transverse vibration whose equation is $y = 0.021\;\sin (x + 30t)$, Where $x$ and $y$ are in meters and $t$ is in seconds. If the linear density of the string is $1.3 \times {10^{ - 4}}\,kg/m,$ then the tension in the string in $N$ will be

The fundamental frequency of a sonometre wire is $n.$ If its radius is doubled and its tension becomes half, the material of the wire remains same, the new fundamental frequency will be

A stretched string of $1m$ length and mass $5 \times {10^{ - 4}}kg$ is having tension of $20N.$ If it is plucked at $25cm$ from one end then it will vibrate with frequency ... $Hz$

Figure shows a snapshot for a travelling sine wave along a string. Four elemental portions $a, b, c$ and $d$ are indicated on the string. The elemental portion which has maximum potential energy is/are

A sonometer wire of resonating length $90 \mathrm{~cm}$ has a fundamental frequency of $400 \mathrm{~Hz}$ when kept under some tension. The resonating length of the wire with fundamental frequency of $600 \mathrm{~Hz}$ under same tension________.$\mathrm{cm}$.

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