What happens when a wave transmits from a denser to rarer medium?

After reflection from the open end, a transverse progressive wave, $y_1=A\sin 2\pi (\frac{t}{T}-\frac{x}{\lambda })$ travels along the direction of negative $x$-axis. The equation of the reflected wave will be,

When a wave is reflected at a rarer surface, the change in phase is

The equation of a wave is $y=A\sin \left(2\pi nt\right)$. When it is reflected at a free end, its amplitude becomes $90\%$. The equation of the reflected Wave is

A string consists of two parts attached at $x=0.$ The right part of the string $(x>0)$ has mass per unit length ${\mu }_y$ and the left part of the string $(\mathrm{x}<0)$ has mass per unit length ${\mu }_1$. The tension in the string is $T$. If a wave of unit amplitude travels along the left part of the string, what is the amplitude of the wave that is transmitted to the right part of the string?

String-$1$ is connected with string-$2$. The mass per unit length in string- $1$ is ${\mu }_1,$ and mass per unit length in string-$2$ is $4{\mu }_1$. The tension in the strings is T.A travelling wave is coming from the left. What fraction of the energy in the incident wave goes into string-2?

A string that is $10 \mathrm{cm}$ long is fixed at both ends. At $t=0$, a pulse traveling from left to right at $1 \mathrm{cm} {\mathrm{s}}^{-1}$ is $4.0 \mathrm{cm}$ from the right end as shown in figure. Determine the next two times when the pulse will be at that point again. State in each case whether the pulse is upright or inverted.

A wave $y_{\mathit{i}}=0.3 \cos (2.0x-40t)$ is travelling along a string toward a boundary at $x=0$. Write expressions for the reflected waves if
(a) the string has a fixed end at $x=0$ and
(b) the string has a free end at $x=0$
Assume SI units.

A wave pulse on a string has the dimensions shown in figure. The wave speed is $v=1 \mathrm{cm} {\mathrm{s}}^{-1}$.

(a) If point $O$ is a fixed end, draw the resultant wave on the string at $t=3 \mathrm{s}$ and $t=4 \mathrm{s}$.
(b) Repeat part (a) for the case in which $O$ is a free end.

When the door of the Chapel of the Mausoleum in Hamilton, Scotland, is slammed, the last echo heard by someone standing just inside the door reportedly comes $15 \mathrm{s}$ later.

$\left(a\right)$ If that echo were due to a single reflection off a wall opposite to the door, how far from the door is the wall ?

$\left(b\right)$ If instead the wall is $32.0 \mathrm{m}$ away, how many reflections (back and forth) occur?

What happens when a wave hits a free end boundary?