Acoustics: Reflection and Transmission Coefficients While studying about reflections and transmission coefficient in a discontinuous Media I came across two definition of coefficients one which seems to be correct according to me as it is in accordance with the physics but there is another definition which I have found in many books and used in many papers. 
Consider a case, when wave is incident from low impedance medium 1 to high impedance medium 2. Then as per my understanding, the amplitude of incident wave should decrease as it goes from low to high impedance ( given by relation 2 below). But if I use relation 1, the amplitude of transmitted wave increases as we go from low to high impedance and that is not possible. 
$Z_1$ and $Z_2$ are impedance of two media


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*Relation 1: 


$$R= \frac{Z_2 - Z_1}{Z_1 + Z_2},\quad   T = \frac{2 Z_2}{Z_1 + Z_2}$$


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*Relation 2: 
$$R = \frac{Z_1 - Z_2}{Z_1 + Z_2},\quad   T = \frac{2 Z_1}{Z1 + Z_2}$$
Could someone please clarify my doubts and discrepancy in the relations that I found?
Reference


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*Kinsler. Fundamentals of Acoustics.



 A: The two expressions look the same to me, with the difference being on the label placed on each medium.
You should focus on the meaning of transmission an reflection coefficient. That is, for a plane wave with unitary amplitude how much of it transfers to the other medium and how much gets reflected. Once you get that, you write down the equations and apply the relations between particle velocity and pressure (given by the characteristic impedance) and boundary conditions. 
This is pretty much what is done in this section of Kinsler's book.
Edit: 2019-06-12

But if I use relation 1, the amplitude of transmitted wave increases as we go from low to high impedance and that is not possible.

Yes, it is possible. The amplitude can go up or down, depending on the impedance contrast. Although, I think I understand what the problem is. You might be thinking that this implies that the power is increasing, but that's not the case. For that, you should look at the intensity (or power) transmission coefficients given by (6.2.10 and 6.2.11):
$$R_I =\left(\frac{Z_2 - Z_1}{Z_2 + Z_1}\right)^2\, ,$$
and
$$T_I = \frac{4 Z_2 Z_1}{(Z_2 + Z_1)^2}\, .$$
Now, $T_I$ cannot increase from one medium to the other but $T$ can. Let us consider $Z_1 = 1$ and $Z_2 = 4$, in that case, we have
$$R = \frac{3}{5}\, ,\quad T = \frac{8}{5}\, ,$$
but,
$$R_I = \frac{9}{25}\, ,\quad T_I = \frac{16}{25}\, .$$
If we change the roles, $Z_1=4$ and $Z_2=1$, we get
$$R = \frac{-3}{5}\, ,\quad T = \frac{2}{5}\, ,$$
but,
$$R_I = \frac{9}{25}\, ,\quad T_I = \frac{16}{25}\, .$$
In the second case, we should interpret the negative sign in the reflection coefficient as a phase change of $\pi$ radians.
Notice that in both cases, the transmitted "energy" is less than 1. But this information is not encoded in the transmission coefficient itself, but in $T_I$. This makes total sense since the impedance is telling us how "easy" is to move the fluid for a given pressure.
