One of the greatest tools in the audiophile toolbox is math. What? Math sucks you say. Well I say get your calculators out and start working your brain. This will be fun, honest.
In retail, chat forums and lunch rooms across the country the single most common questions are “how do I get my system louder” or “how loud will these subs be”. I can personally guarantee you that you ask ten people this question, including the guys at the stereo shop, you will get 13 different answers and none of them will be basing their answers on facts. They simply do not know how it works. There are some basic physics at work here.
Volume, which is measured in decibels (expressed by dB), is a function of power, cone area, enclosure design, and transfer function. Oh, you knew that already? Ok, sure that last statement might seem a little obvious, but undestanding how they interact togethr is critical to calculating volume. That’s right, you can calculate exactly how loud you system will be. Enough BS, here is the worksheet. You won’t find this anywhere else, send your friends.
This formula requires a few specs. First, you need the sensitivity of the sub(s). This listed on the woofer spec sheet in dB. It is sometimes notated as the SPL of the sub. Next, you need to know how much power your amp puts out. An amp birth-sheet (usually included in the box) will have the actual power the amp displayed when it was tested at the factory. Not all amps come with these. If you do not have such a sheet, you can use the power ratings, or even better, you can test it yourself (that is whole other enchilada and we will get into that another time). Other specs you need are more simple- what type of car do you have- truck, hatchback, or sedan; and what kind of box is it installed in. The enclosure will make a big difference, if it is a crappy home-built box with lots of leaks, held together with carpet and liquid nails, it probably won’t function as well as a professionally-built enclosure (like the Q-Logic pre-fab enclosures- shameless plug) and how many woofers you have. Have fun.
Every time the cone area doubles, the output of the system increases by 3 dB, which is relative to a doubling of volume. If you have 4 subs, you would add 9 dB to the sensitivity rating of the subwoofers.
add 3 dB per doubling of cone area
i.e. 2 subs, 3 dB, 4 subs, 6 dB
Let’s consider sub sensitivity, with 3 dB per sub added and calculate the SPL. Each time the output power (wattage) of the amplifier doubles, the SPL increases by 3 dB. To figure this, use the following figures.
This represent 3 dB added per doubling of power starting at 1 watt/meter SPL.
Next we add in Transfer Function
add 12 dB for a standard car/truck
add 16 dB for a hatchback car
Now we figure in box type
For a sealed box, 0 dB, sealed offers no dB gain.
For a ported box, 3-9 dB depending on tuning frequency and air ripple. The higher the ripple, the more gain but at a cost of sound quality.
For a bandpass box, 6-12 dB again depending on the tune freq. and ripple.
For example, a 12″ Rockford Fosgate subwoofer has a sensitivity of 86 db at 1 watt/1 meter, and is capable of handling 300 watts.The sub is installed in a ported enclosure, so we are going to use a the lower output rate for the ported box at 3 dB. Powering the subwoofer is a Rockford Fosgate Punch 300-1, which is rated at 300 watts to a single 4-ohm load. All of this is installed in a 2006 Honda Civic Si, which is a hatchback and gets a boost from the 16 dB transfer function. Using the formula, we get the following results-
86+ 24 (at 256 watts, it is close, but you could add in an extra dB if you want) + 16 (trans function) + 3 (box gain) = 129 dB estimated output. This estimation will be within +\- 3 dB of the measured output. This is simple physics, and it works.