$A$ steel wire of length $81 \text{ cm}$ has a mass of $5 \times 10^{-3} \text{ kg}$. If the wire is under a tension of $50 \text{ N}$, then the speed of transverse waves on the wire is (in $\text{ m s}^{-1}$)

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:

$A$ string of mass $M$ and length $L$ hangs freely from a fixed point. The velocity of a transverse wave along the string at a distance $x$ from the free end will be:

$A$ string wave equation is given by $y=0.002 \sin (300 t-15 x)$ and the linear mass density is $\mu=0.1 \ kg/m$. Find the tension in the string (in $N$).

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

The linear density of a vibrating string is $1.3 \times 10^{-4} \, kg/m$. $A$ transverse wave is propagating on the string and is described by the equation $Y = 0.021 \, \sin(x + 30t)$,where $x$ and $y$ are measured in meters and $t$ in seconds. The tension in the string is ..... $N$.