Click here to purchase the entire book in PDF format. Intuitive Acoustic Resistance Get a dinner plate and hold it with two hands in front of you like you're holding the steering wheel of a car as is shown in Figure . STICK FIGURE TO GO HERE Without turning your plate, push it away from you, then pull it back towards you closer than where you started, then push it back out and so on. Figure 3.16 shows the displacement of the plate relative to the resting position. A positive displacement means that the plate is further away from you than the resting position, a negative displacement means that it's closer. We can also think about the velocity of the plate. Velocity is a little like speed except that it's smarter. Speed tells you how fast you're moving (how much distance you're travelling in an amount of time). Velocity tells you the same thing, but it also tells you in what direction you're moving. For example, if we say that positive velocity is forwards, then if you're going backwards, you must have negative velocity. It's possible in a car to have a velocity of -10 km/h, but you can never have a speed of -10 km/h. This is because speed is just distance travelled in time, and you can't move -10 km. So, back to the plate. If we graph the velocity of the plate in relation to its displacement we'll get Figure 3.16. Now get into a large swimming pool holding your plate and do the same thing, pushing and pulling the plate further away from and closer to you. Think about how hard it is to push and pull the plate in the water. This is obviously because in pushing the plate, you have to push the water out of the way. If I asked you to get in a swimming pool full of oil, it would be harder still to push and pull the plate. In air, it's quite easy. However, I'm not really concerned at this point about how hard it is to push and pull the plate. We're more interested in the specifics of when you push and when you pull. Let's go back to the swimming pool, and assume that you've already been pushing and pulling your plate for a while. People have given up staring at you and gone back to their water-volleyball game, and you're left alone to concentrate. As you move the plate away from you, no matter where the plate is, you're pushing. If you're moving the plate towards you, you're pulling. (This may seem obvious at the moment, but you have to bear with me... You'll see in a moment why I'm stating the stupid...) There's a graph showing this relationship in Figure 3.16 Figure 3.16: The relationship between the displacement of a dinner plate, its velocity and the force you have to apply to keep it moving while you're in a swimming pool. Ignore the vertical scale of these three plots - just think about their shape and polarities. Positive displacement is further away from you. Positive velocity is moving away from you. Positive force is you pushing - negative indicates that you're pulling. What does Figure 2.14 tell us? We can see that the effort that you're putting into your plate is in phase with the velocity of the plate. If the velocity is positive (in other words, if the plate is moving away from you) then you're pushing it. If the velocity is negative (if the plate is moving towards you) then you're pulling it. You'll also note that if your effort is proportional to the plate's velocity (in other words, you have to work harder to move the plate faster). You should also note that your effort (and the plate's velocity) is 90$^\circ$ out of phase with the plate's displacement. When the displacement is at maximum (when the plate is farthest away), the plate's velocity and your effort level are zero. The same is true when the displacement is minimum (the plate is nearest). When the displacement is zero (the plate is at the starting point) then the velocity and your effort are at a maximum (or a minimum, depending on direction). Let's go back briefly to the swimming pool filled with oil. All of the discussion of whether you're pushing or pulling will all hold to be true. The only thing that will change is how hard you have to push and pull. This is because oil is thicker and therefore harder to move than water.