Click here to purchase the entire book in PDF format. Intuitive Acoustic Reactance Okay, okay... that previous section in the swimming pool might have seems like a total waste of your time. However, hopefully, this section will change your mind. Take your dinner plate from section 3.1.23 and get out of the pool. Find a large, concrete wall and attach a spring to it. Then attach your plate to the other end of the spring as is shown in Figure FIGURE SHOWING WALL, SPRING AND DINNER PLATE. Now hold your dinner plate the way you did in the previous section and push and pull it, moving it back and forth the way you did in the pool. The displacement and the velocity of the plate are the same as they were in the pool, represented by the graph in Figure 3.17. However, if you're paying attention, you'll notice that your behaviour has changed. When the plate is moving away from you (therefore having an increasing positive displacement), you're pushing it. So far so good. Then you get as far away as you can get with the plate. The displacement is at a maximum and the velocity is zero, just like in the pool. However, unlike when you're in the pool, you're still pushing. If you stopped pushing, the plate would spring back - you have to push just to keep the plate that far away because the spring is pushing back towards you. As the plate comes back towards where it started, you're still pushing. This is a strange situation - you're pushing, but the plate is moving towards you - but you have to push against the spring. When the plate returns to its starting point, you neither push nor pull because the spring is holding the plate there for you. Then, as you move the plate towards you, you pull on it until it's as close as it's going to get. The displacement is at a minimum, the velocity is zero, and you're pulling as hard as you can. As the plate moves back out away from you again, its displacement returns to zero, its velocity is positive, but you're still pushing. All of this is shown in Figure 3.17 Figure 3.17: The relationship between the displacement of a dinner plate, its velocity and the force you have to apply to keep it moving if the plate is glued to a spring sticking out of a wall. 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. The interesting thing is to compare Figure 3.16 to Figure 3.17. Notice that the relationship between the plate's displacement and its velocity has not changed. They're always 90$^\circ$ out of phase. However, what changes is your effort. In the case of the swimming pool, your effort was in phase with the displacement. In the case of the spring, your effort was in phase with the displacement. Most importantly, your effort in the swimming pool was 90$^\circ$ out of phase from your effort with the spring. The other important thing to note here was the issue of conservation of energy (time to think back to potential and kinetic energy). In the case of the pool, your energy was directly converted into kinetic energy - you push and the plate moves. This is why the velocity and your effort in the pool are in phase. If your effort goes up, the velocity (and therefore the kinetic energy) of the plate goes up. However, if you stop pushing, the plate stops moving. You are not storing any potential energy in the plate. In the case of the spring, you push and put potential energy into the spring. The harder you push, the more energy the spring has to push back. This is why your effort is 90$^\circ$ out of phase with the velocity. It's because you're not making the plate move. You're putting potential energy into the spring and it's moving the plate.