Few doubts regarding waves acting on strings First let's take a look at the image  below

XY and YZ are two different strings. Strings XY and YZ are connected each other at Y.

Now what I do is, I create a wave pulse by shaking the composite  string from the end X by   using my hand. Assume the wave pulse that I am created is  same  as the one in the below  image.(Note: Assume I hold the string with my hand until this  experiment is finished )

So what I want to know is what would be the resultant shape of wave when it reaches Y on strings XY and   YZ, if 
1. Mass per unit length of string XY > Mass per unit length of string
    YZ.
2.  Mass per unit length of string XY < Mass per unit length of string
    YZ.

And further I want to know how a pulse  that is slanted to one side behave under these conditions (The conditions that mentioned just above this paragraph )
Like these,

.
 A: Well you are going to get a reflected and transmitted wave, the two properties that change from the original input wave are the amplitude and wavelength of the two waves.
I am going to use 1 and 2 to denote the input side of the string and transmission side respectively. 
Amplitude
The amplitude is determined by these two formulae:
$$A_r=A_i \frac{Z_1 - Z_2}{Z_1+Z_2}$$
$$A_t=A_i\frac{2Z_1}{Z_1+Z_2}$$
Where $Z=\sqrt{Tμ}$; $μ$ is the mass per unit length of the string and $T$ is the tension in the string.
As the tension has to be the same all the way down the string we can remove $T$ from the above formulae for $A_r$ and $A_t$.
$$A_r=A_i \frac{\sqrt{μ_1} - \sqrt{μ_2}}{\sqrt{μ_1}+\sqrt{μ_2}}$$
$$A_t=A_i\frac{2\sqrt{μ_1}}{\sqrt{μ_1}+\sqrt{μ_2}}$$
Wavelength
$$c=\sqrt{\frac{T}{μ}}=fλ$$
Now at the intersection the waves have to agree, so $f$(frequency of the wave) is the same for the transmission wave and the reflection wave. $T$ has already been establish as the same through out.
$$λ_1 = \frac{\sqrt{\frac{T}{μ1}}}{f}$$
$$λ_2 = \frac{\sqrt{\frac{T}{μ2}}}{f}$$
This won't change the reflected wave as it does not change medium. But as the transmitted wave goes from the medium with density $μ_1$ to $μ_2$ it will change wavelength.
From these formulae we can now outline the two cases.
Case 1($μ1 > μ2$)
$A_r$ is negative and less than $A_i$(in magnitude).
$A_t$ is greater than $A_i$.
$λ_t$ is greater than $λ_r$.
Case 2($μ1 < μ2$)
$A_r$ positive and still less than $A_i$.
$A_t$ positive and less than $A_i$.
$λ_t$ is less than $λ_r$.
Slanting
Also the slanting will look the same except for the slant.
