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

A wire of density $8 \times 10^3\,kg / m ^3$ is stretched between two clamps $0.5\,m$ apart. The extension developed in the wire is $3.2 \times 10^{-4}\,m$. If $Y =8 \times 10^{10}\,N / m ^2$, the fundamental frequency of vibration in the wire will be $……\,Hz$.

A uniform metal wire of density $\rho $, cross-sectional area $A$ and length $L$ is stretched with a tension $T$. The speed of transverse wave in the wire is given by

A string of length $1\,\,m$ and linear mass density $0.01\,\,kgm^{-1}$ is stretched to a tension of $100\,\,N.$ When both ends of the string are fixed, the three lowest frequencies for standing wave are $f_1, f_2$ and $f_3$. When only one end of the string is fixed, the three lowest frequencies for standing wave are $n_1, n_2$ and $n_3$. Then

A sonometer wire, with a suspended mass of $M = 1\, kg$, is in resonance with a given tuning fork. The apparatus is taken to the moon where the acceleration due to gravity is $(1/6)$ that on earth. To obtain resonance on the moon, the value of $M$ should be ……… $kg$