$A$ uniform rope of mass $6\,kg$ hangs vertically from a rigid support. $A$ block of mass $2\,kg$ is attached to the free end of the rope. $A$ transverse pulse of wavelength $0.06\,m$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top is (in $m$):

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4\, \%$,will be ......... $\%$

Two strings $A$ and $B$ of the same material are stretched by the same tension. The radius of string $A$ is double the radius of string $B$. $A$ transverse wave travels on string $A$ with speed $V_A$ and on string $B$ with speed $V_B$. The ratio $\frac{V_A}{V_B}$ is:

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:

$A$ steel wire has a length of $12.0 \;m$ and a mass of $2.10 \;kg$. What should be the tension in the wire so that the speed of a transverse wave on the wire equals the speed of sound in dry air at $20\,^{\circ}C = 343 \;m s^{-1}$?

$A$ transverse wave propagating on a stretched string of linear density $3 \times 10^{-4} \ kg \ m^{-1}$ is represented by the equation $y = 0.2 \sin (1.5 x + 60 t)$,where $x$ is in metres and $t$ is in seconds. The tension in the string (in newton) is