Click here to purchase the entire book in PDF format. Reflection and Transmission Coefficients RE-WRITE THIS SECTION The ratios of reflected and transmitted pressures to the incident pressure are frequently expressed as the pressure reflection coefficient, $\textbf{R}$ , and pressure transmission coefficient, $\textbf{T}$ , shown in Equations 3.28 and 3.29 [Kinsler and Frey;, 1982]. $$\textbf{R} = \frac{\textbf{P}_{r}}{\textbf{P}_{i}}$$ (4.28) $$\textbf{T} = \frac{\textbf{P}_{t}}{\textbf{P}_{i}}$$ (4.29) What use are these? Well, let's say that you have a sound wave hitting a wall with a reflection coefficient of $\textbf{R} = 1$. This then means that $\textbf{P}_{r} = \textbf{P}_{i}$, which is a mathematical way of saying that all of the sound will bounce back off the wall. Also because of Equation 3.25, this also means that none of the sound will be transmitted into the wall (because $\textbf{P}_{r} = 0$ and therefore $\textbf{T} = 0$), so you don't get angry neighbours. On the other hand, if $\textbf{R} = 0.5$, then $\textbf{P}_{r} = \frac{\textbf{P}_{i}}{2}$ which in turn means that $\textbf{P}_{r} = \frac{\textbf{P}_{i}}{2}$ (and therefore that $\textbf{T} = 0.5$) and you might be sending some sound next door... although we would have to do a little more math to really decide whether that was indeed the case. Note that the pressure reflection coefficient can either be a positive number of a negative number. If $\textbf{R}$ is a positive number then the pressure of the reflection will have the same polarity as the incident wave, however, if $\textbf{R}$ is negative, then the pressures of the incident and reflected waves will have opposite polarities. THINK BACK TO THE EXAMPLE WITH YOUR FRIENDS...