Transmission of waves How do you know if a wave will transmit when it hits a media boundary? Will a portion of the wave always be transmitted when a wave hits a media boundary? My textbook says part of the wave will be transmitted when the media boundary is neither free-end nor fixed-end.
It says a free-end reflection occurs when a wave is going from a slowed medium to a faster medium, and fixed-end reflection occurs when the opposite is true. How can a medium not be free-end or fixed-end?
What is considered free-end, and what is considered fixed-end?
 A: I will attempt to address one of your questions:

So what is considered free end, and what is considered fixed end

Picture an ideal string fixed at one end.  Since the end is fixed, the displacement of the string there must be zero.

Now, picture a string with an end that is free to move in the direction of the displacement.  That is a free end.

Take a look at this animation and see the result of a wave impinging on both a fixed end and a free end.
A: Another way to look at it.  If we have two media with two different transmission coefficients, $Z_1$ and $Z_2$, we know that we have to account for all three parts of our incoming wave, so
$$ 1 + R = T $$
where on the left of the boundary we have our incident wave (1) and the reflected bit $R$ and on the right of the boundary we have our transmitted wave $T$.  And as is done in any waves book by matching the actual values of the wave and its derivative at the boundary you can show that in general.
$$ R = \frac{ Z_1 - Z_2 }{ Z_1 + Z_2 } $$ so that
$$ T = \frac{ 2 Z_1 }{ Z_1 + Z_2 } $$
The fixed and free boundary conditions correspond to the two natural limits $ Z_2 \gg Z_1,  Z_2 \ll Z_1 $, or if you like, as $Z_2$ approaches infinity or zero.  In which case you get
$$ Z_2 \to \infty \qquad R \to -1 \quad T \to 0 $$
which corresponds to the first of Alfred's pictures and
$$ Z_2 \to 0 \qquad R \to 1 \quad T \to 2 $$
which corresponds to the second of Alfred's pictures.  The $T=2$ might seem odd, but if you watch the animation Alfred links to, you can see the ring undergoes twice the displacement of the wave.
So, in general there is always some portion of a wave that is transmitted at the boundary of two media.
