Click here to purchase the entire book in PDF format. Acoustic Impedance Revisited Get about 20 of your closest friends together and stand, single file in a line. Everybody has already agreed to not get in a fight over this one... Each person puts their hands on the shoulders of the person in front of them. The deal is that, if the person behind you pushes you forward, you push the person ahead of you with the same force as you you were pushed. One last thing: get the person at the front of the line to put their hands on a concrete wall. The person at the back of the line pushes the person in front of him, and that person, in turn, pushes the person in front of her and so on and so on. So, each person in the line is falling forward by as much as they were pushed. Finally, the person at the front of the line gets pushed and pushes back against the concrete wall. As a result, she falls backwards, pushing the person behind her backward who falls back and pushes the person behind him backwards and so on until we get back to the back of the line. There are a number of different things to notice here: Each person in the line can push the person directly in front of him or her exactly as hard has he or she was pushed. The person at the front of the line can't move the concrete wall, so she winds up pushing herself backwards when she was pushed by the person behind her. The person at the back of the line originally pushed forwards, but after the whole chain reaction has happened, he gets pushed backwards - in the opposite direction to that in which he pushed in the first place. Finally, the chain reaction reversed direction at the wall. This isn't saying the same thing as the previous point. What I mean is that, before the wall, each person was affecting the person in front, but after the wall, each person was affecting the person behind. Now, repeat this whole process, but have the person at the front of the line stand in an open doorway instead of putting her hands on a concrete wall. The person at the back of the line pushes the person in front who pushes the person in front and so on until the front person is pushed forward. Because she has nothing to push against, she winds up falling forward. This pulls the person behind her forwards who pulls the person behind him forwards and so on. The points to pay attention to here are: Just like the first situation, each person in the line can push the person directly in front of him or her exactly as hard has he or she was pushed. The person at the front of the line doesn't have anything to push, so she falls forwards. The person at the back of the line originally pushed forwards, and after the whole chain reaction has happened, he gets pulled forwards - in the same direction to that in which he pushed in the first place. Again, the chain reaction reversed direction at the open door in exactly the same way as it did with the wall. Why have I drawn this picture for you? Replace each person in the line with an air molecule. When you push a molecule forward, it pushes the adjacent molecule in the same direction which continues the same chain reaction. Notice here that each molecule can push its adjacent molecule easily - in fact, there is nothing at all stopping it from moving forwards and pushing. Eventually, if we get to the last molecule in the line and it's up against a concrete wall (or at least something that's harder to move than another air molecule) then it winds up pushing back against the molecule behind it and so on. So, we pushed an air molecule forwards, but after the chain reaction, it gets pushed back towards us in the opposite direction. If, however, the molecule down at the end is standing in the equivalent of an open doorway, then it falls out, pulling the molecule behind it int he same direction. We pushed the first molecule forward, and eventually, it gets pulled forwards by the molecule in front. To oversimplify a little bit, what we're really talking about here is called acoustic impedance. This is a measure of how easily an air molecule can push or pull whatever is next to it (actually, how much the movement is restriced or impeded). If it's another air molecule, then it can push as easily as it was pushed. If it's concrete, then it can't push as easily. The higher the acoustic impedance, the harder it is to move the molecule. This was discussed in more detail in the previous chapter. As we change materials, we change the acoustic impedance, however, we can also change the acoustic impedance of a material by changing its environment. For example, it is harder to push air molecules when they're in a tube than when they're in a free field, therefore, the acoustic impedance of air inside the tube is higher than it is in the outside world. How do we measure how hard it is to move something? Well, let's think about trying to push a car, let's say. You push on the car with an amount of pressure, and the car moves forward at a certain speed. If you push wheelbarrow with the same pressure, it will move faster (assuming that a wheelbarrow is easier to push than a car...) This relationship is used to determine the acoustic impedance of a given medium. Take a look at Equation 3.15. $$z = \frac{p}{u}$$ (4.15) where $z$ is the acoustic impedance of the material measured in N s/m$^3$ (Newton seconds per meter cubed)4.2, $p$ is the pressure applied to the molecules in the medium in Pascals and $u$ is the velocity of the air molecules in m/s. What this equation tells us is if you have a wavefront with the same pressure in two different substances with two different acoustic impedances, then the particle velocity will be higher in the material with the lower impedance.