When a wave travels from a denser to rarer medium, then

Incident wave $\mathrm{y}=\mathrm{A} \sin \left(\mathrm{ax}+\mathrm{bt}+\frac{\mathrm{\pi }}{2}\right)$ is reflected by an obstacle at $\mathrm{x}=0$ which reduces intensity of reflected wave by $36\%.$ Due to superposition, the resulting wave consists of a standing wave and a travelling wave given by $\mathrm{y}=-1.6 \mathrm{sinax} \mathrm{sinbt}+\mathrm{cA} \cos (\mathrm{bt}+\mathrm{ax})$ where $\mathrm{A}, \mathrm{a}, \mathrm{b}$ and c are positive constants.

Amplitude of reflected wave is

Incident wave $\mathrm{y}=\mathrm{A} \sin \left(\mathrm{ax}+\mathrm{bt}+\frac{\mathrm{\pi }}{2}\right)$ is reflected by an obstacle at $\mathrm{x}=0$ which reduces intensity of reflected wave by $36\%.$ Due to superposition, the resulting wave consists of a standing wave and a travelling wave given by $\mathrm{y}=-1.6 \mathrm{sinax} \mathrm{sinbt}+\mathrm{cA} \cos (\mathrm{bt}+\mathrm{ax})$ where $\mathrm{A}, \mathrm{a}, \mathrm{b}$ and c are positive constants.

Value of $c$ is

Position of second antinode is

Three pieces of string, each of length $L$, are joined together end-to-end, to make a combined string of length $3L$. The first piece of string has a mass per unit length ${\mu }_1,$ the second piece has a mass per unit length ${\mu }_2=4{\mu }_1$ and the third piece has a mass per unit length ${\mu }_3={\mu }_1/4$ 

$\left(\mathrm{a}\right)$ If the combined string is under tension $F$, how much time does it take a transverse wave to travel the entire length $3L ?$ Give your answer in terms of $L, F$ and ${\mu }_1$.
$\left(\mathrm{b}\right)$Does your answer to part (a) depend on the order in which the three pieces are ioined together? Explain.