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:

Which of the following is an example of a transverse wave?

Consider a system of three connected strings,$S_1, S_2$ and $S_3$ with uniform linear mass densities $\mu \text{ kg/m}$,$4\mu \text{ kg/m}$ and $16\mu \text{ kg/m}$,respectively,as shown in the figure. $S_1$ and $S_2$ are connected at the point $P$,whereas $S_2$ and $S_3$ are connected at the point $Q$,and the other end of $S_3$ is connected to a wall. $A$ wave generator $O$ is connected to the free end of $S_1$. The wave from the generator is represented by $y = y_0 \cos(\omega t - kx) \text{ cm}$,where $y_0, \omega$ and $k$ are constants of appropriate dimensions. Which of the following statements is/are correct:
$(A)$ When the wave reflects from $P$ for the first time,the reflected wave is represented by $y = \alpha_1 y_0 \cos(\omega t + kx + \pi) \text{ cm}$,where $\alpha_1$ is a positive constant.
$(B)$ When the wave transmits through $P$ for the first time,the transmitted wave is represented by $y = \alpha_2 y_0 \cos(\omega t - kx) \text{ cm}$,where $\alpha_2$ is a positive constant.
$(C)$ When the wave reflects from $Q$ for the first time,the reflected wave is represented by $y = \alpha_3 y_0 \cos(\omega t - kx + \pi) \text{ cm}$,where $\alpha_3$ is a positive constant.
$(D)$ When the wave transmits through $Q$ for the first time,the transmitted wave is represented by $y = \alpha_4 y_0 \cos(\omega t - 4kx) \text{ cm}$,where $\alpha_4$ is a positive constant.

Transverse waves of the same frequency are generated in two steel wires $A$ and $B$. The diameter of $A$ is twice that of $B$,and the tension in $A$ is half that in $B$. The ratio of the velocities of the waves in $A$ and $B$ is:

$A$ uniform metal wire of length $L$,mass $M$,and density $\rho$ is under a tension $T$. If the speed of a transverse wave along the wire is $V$,then the area of cross-section of the wire is:

$A$ uniform rope having some mass hangs vertically from a rigid support. $A$ transverse wave pulse is produced at the lower end. The speed $(v)$ of the wave pulse varies with height $(h)$ from the lower end as: