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

The fundamental frequency of vibration of a string stretched between two rigid supports 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 produced in the string is $..........\,m/s$.

The equation of a transverse wave propagating along a stretched string of length $80 \ cm$ is $y=1.5 \sin \{(5 \times 10^{-3} x) + 20 t\}$,where $x$ and $y$ are in $cm$ and the time $t$ is in seconds. If the mass of the string is $3 \ g$,then the tension in the string is: (in $N$)

Write the equation for the speed of a transverse wave on a stretched string.

Two strings $(A, B)$ having linear densities $\mu_{A} = 2 \times 10^{-4} \ kg/m$ and $\mu_{B} = 4 \times 10^{-4} \ kg/m$ and lengths $L_{A} = 2.5 \ m$ and $L_{B} = 1.5 \ m$ respectively are joined. Free ends of $A$ and $B$ are tied to two rigid supports $C$ and $D$, respectively, creating a tension of $500 \ N$ in the wire. Two identical pulses, sent from $C$ and $D$ ends, take time $t_1$ and $t_2$, respectively, to reach the joint. The ratio $t_1 / t_2$ is:

$A$ heavy rope is suspended from a rigid support. $A$ transverse wave pulse is set up at the lower end,then