Boyles Law, how it applies to an SPL system

This article comes to you courtesy of JBL. It explains Boyles law, its applications in car audio and how it explains various phenomena in car audio. If you dont know this, you should.

There are several ways to alter the pressure inside any closed space. Air compressors use a piston and a valve to force additional air into the tank without allowing air to escape, but the tank always maintains its size. When we use a speaker to pressurize the air inside a cavity, like the space within a car, we pressurize the air according to Boyle's Law. Boyle's Law states that the change pressure is inversely proportional to the change in volume. P1/P2 = V2/V1 When the speaker cone moves forward (into the cavity) the pressure increases as the cavity volume decreases.

The amount of the pressure change depends upon the amount of air the woofers can displace. The distance the cone moves forward times the area of the cone determines the displacement of the speaker. So, how does this relate to pressurizing the cab of a car' Obviously, and from Boyle's Law, the greater the reduction in volume, the greater the increase in pressure. Shoehorning as many woofers in the smallest space possible and driving them with as much power as possible will provide the highest pressure if you are designing an SPL competition vehicle using sealed enclosures. What we have to consider, and what will help us to understand what happens when we use a vented box for SPL competition, is where will the highest pressure be' Consider the following: If the motor of the speaker provides force to pressurize the air in a box, there will be some amount of compression (of the air within an enclosure) which will have a restoring force equal the maximum force that can be applied by the speaker's motor. One of the reasons that we choose a sealed box for non-competition systems is because the excursion of the woofer is limited by the pressure inside the box, which helps the woofer handle more power at the lowest frequencies. It's a benefit of using sealed boxes for music reproduction, but may be a detriment for SPL competition systems that use sealed boxes. The pressurized air inside the box limits the woofer's excursion because, with high input power, the force of the motor isn't great enough to overcome the force exerted by the pressurized air inside the box. When the woofer reaches that point, it can't move any farther or play any louder. This principle assumes that the woofer has enough excursion potential to reach this point. If not, the maximum pressure possible will be determined by the physical limits of the motor's travel. Since the area that we want to pressurize is one box (the cab of the car), and the box that contains the speakers is another box, Boyle's Law indirectly states that the higher pressure will be present in the smaller of the two boxes. No matter how you design your system, it will be a combination of several enclosures with a speaker(s) mounted between them and the pressure will always be greatest in the smallest box driven by the same diaphragm.

You can prove this easily. Build a sealed box for any woofer and install the woofer. Drill a small hole in the box, just big enough to insert the tip of a microphone all the way into the box. Energize the woofer at some frequency and measure the pressure. Pull the microphone out, seal the hole, place the box inside a car and measure the pressure inside the car at the same frequency and at the same drive level. The pressure in the enclosure will exceed the pressure inside the cab of the car.

Not only does Boyle's law define this phenomenon, but it may also be used to quantify it. The difference in pressure as a percent will be equal to the difference in volume as a percent. Following Boyle's Law, we can be sure that to maximize the amount of pressure in the cab of the vehicle, the cab should be smaller than the box that contains the woofers. Essentially, the cab should be as small as possible and the space behind the baffle should be at least as big as the cab.

If you've installed a few subwoofer systems, you may have experienced an increase in the amount of bass produced by the system when the vehicle's trunk or a window is opened. I've heard some fantastic explanations for this 'problem'. The fact is, that when the window or the trunk is opened, a port is created, and the pressure inside the car increases as a result of the additional acoustic load, just like in a vented box, and according to the principles of Helmholtz resonance. Manipulating this phenomenon is the best way to build SPL competition cars. Since we know that (1) pressure is always greatest in the smallest of the boxes (2) pressure is greater in a vented box than a sealed box of the same volume, and (3) at Fb, when the woofer moves the least, it's operating most efficiently, the choice of enclosure type is obvious: vented enclosures are the ones to use.