$A$ copper wire is held at the two ends by rigid supports. At $50^{\circ} C$ the wire is just taut,with negligible tension. If $Y=1.2 \times 10^{11} \, N/m^2$,$\alpha=1.6 \times 10^{-5} /^{\circ} C$,and $\rho=9.2 \times 10^3 \, kg/m^3$,then the speed of transverse waves in this wire at $30^{\circ} C$ is .......... $m/s$.

$A$ sitar wire is replaced by another wire of same length and material but of three times the earlier radius. If the tension in the wire remains the same,by what factor will the frequency change?

$A$ rope of length $L$ and uniform linear density is hanging from the ceiling. $A$ transverse wave pulse,generated close to the free end of the rope,travels upwards through the rope. Select the correct option.

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 $0.1 \, kg$ is under a tension $1.6 \, N$. The length of the string is $1 \, m$. $A$ transverse wave starts from one end of the string. The time taken by the wave to reach the other end is (in $s$.)

$A$ 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 $20\,^{\circ}C = 343 \;m s^{-1}$?