Click here to purchase the entire book in PDF format. Power So far, we've looked at a number of different ways to measure the level of a sound. We've seen the pressure, the particle displacement and velocity and some associated measurements like the SPL. These are all good ways to get an idea of how loud a sound is at a specific point in space, but they are all limited to that one point. All of these measurements tell you how loud a sound is at the point of the receiver, but they don't tell you much about how loud the sound source itself is. If this doesn't sound logical, think about the light radiated from a light bulb - if you measure that light from a distance, you can only tell how bright the light is where you measure it, you can't tell the wattage of the bulb (a measure of how powerful it is). We've already seen that the particle velocity is proportional to the pressure applied to the particles by the sound source. The higher the pressure, the greater the velocity. However, we've also seen that, the greater the acoustic impedance, the lower the particle velocity for the same amount of pressure. This means that, if we have a medium with a higher acoustic impedance, we'll have to apply more pressure to get the same particle velocity as we would with a lower impedance. Think about the pendulums again - if we have a heavy and a light one and we want them to have the same velocity, we'll have to push harder on the heavy one to get it to move as fast as the light one. In other words, we'll have to do more work to get the heavy one to move as fast. Scientists typically don't like work - otherwise they would have gotten a job in construction instead... As a result, they even use a different word to express work - specifically, they talk about how much work can be done using power. The more power you have in a device, the more work it can do. This can be seen from day to day in the way light bulbs are rated. The amount of work that they do (how much light and heat they give off) is expressed in how much power they use when they're turned on. This electrical power rating (expressed in Watts) is discussed in Section 2.2. THE FOLLOWING IS A BIG LEAP In the case of acoustics, the amount of work that is done by the sound source is proportional to the force applied to particles and the resulting particle velocity - the more pressure and/or the more velocity, the more work you had to do to achieve it. Therefore the acoustic power measured at a specific point in space is proportional to the square of the acoustic pressure. Remember that the change in pressure is a result of the work that is done - you put power into the system and you get a change in power as an output. This relationship between acoustic power and acoustic pressure is moderately useful in that it gives us an idea of how much work is being done to move a measurement device (a microphone diaphragm), but it still has a couple of problems. Firstly, it is still a measurement of a single point in space, so we can only see the power received, not the total power radiated by the sound source. Another problem with power measurements is that they can't give you a negative value. This is because a positive pressure produces a positive velocity and when the two are multiplied we get a positive power. A negative pressure multiplied by a negative velocity also equals a positive power. This really makes intuitive sense since it's impossible to have a negative amount of work, which is why we need power and pressure measurements in many cases - we need the latter to find out what's going on on the negative side of the stasis pressure.