# Sound wave travelling from high impedance to low impedance medium, what will be the reflection & transmission coeffiecient?

Let us assume that a wave propagates in the direction perpendicular to the flat surface of discontinuity. When the characteristic impedance of the medium of medium 0 (where the incident and reflected wave exists) is mush larger than medium 1 (where the transmitted wave exists). How do the pressure and intensity reflection and transmission coefficient behave?

I believe that in this case, the power will not be transmitted. And all the sound waves will turn into reflection.

I don't know how to represent it math terms for R and $$\tau$$.

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. Dec 23, 2021 at 11:02

Assuming that your media have characteristic acoustic impedances $$r_0$$ and $$r_1$$ you end up with the following reflection and transmission coefficients

\begin{align} &R = \frac{r_1 - r_0}{r_1 + r_0}\, , \\ &T = \frac{2r_1}{r_1 + r_0}\, . \end{align}

The intensity reflection and transmission coefficients are

\begin{align} &R_I = \left(\frac{r_1 - r_0}{r_1 + r_0}\right)^2\, , \\ &T_I = \frac{4 r_1 r_0}{(r_1 + r_0)^2}\, . \end{align}

You can see that the intensity reflection coefficient does not depend on the sign of $$r_1 - r_0$$, that is, it does not matter which one is larger. The same power is reflected. The reflection coefficient does depend on the sign of $$r_1 - r_0$$ and it tells us something about the (relative) phase of the reflected wave.

For more detail I suggest checking the following reference:

• Kinsler, L. E., Frey, A. R., Coppens, A. B., & Sanders, J. V. (2000). Section 6.2 in Fundamentals of acoustics. John wiley & sons.