Measuring Transfer Function, Boundary Loading & Soundwaves
27th of January 2009
Ever wonder why a box can sound great in a car but crappy in your garage or even in a car audio shop? The reason why subwoofers sound louder and better in vehicle is due to Transfer Function. TF is a phenomenon caused by vehicle resonances, boundary loading, reflections and absorptions.
Virtually every vehicle, room or chamber has signature TF. Obviously if you play a 15” sub in an open field, it will not be nearly as loud as in a much smaller vehicle, but TF also “amplifies” the output at a certain rate beginning at a certain frequency per vehicle.
TF also affects midbass, midrange and tweeter frequencies, but we won’t go there as the subs have the significant impact on the system as far as TF is involved.
TF not only causes high gains in the sub region, but it also causes problem with excessive peaks and troughs. Knowing how to take advantage of a vehicle’s TF can significantly improve the overall performance of the system! To take advantage of TF, you first need to be able to figure out what the signature TF is for the vehicle you’re working on. There are a couple of ways to do it, but to make it cheap and easy for you, you’ll need the following:
1. An SPL meter - $30-$40 at Radio Shack
2. A test tone CD
3. Frequency graph or make your own
4. Patience – it takes a little while…
Basically what we are going to do is map the response of a subwoofer box by itself. Then we’ll map it inside the vehicle. The difference is your TF! Pretty easy, huh?
Ideally, you’d have a sound proof room or anechoic chamber to get the un infected response of the sub box. Since that isn’t going to happen, you need to be somewhere far away from any buildings, highways, etc. Find a huge open field or something that is as quiet as possible. Elevate the box if at all possible. A yard or meter above the ground would be best. Next, put in your CD and set the volume to the sub at a moderate level and make sure that the lowest and highest frequencies of your test CD will register on the meter. It may take a bit of screwing around until you find a good level/setting. Please understand that people can’t hear under 20Hz, so do not worry if these are not loud enough to register on the meter. We can guesstimate that part later… Take your frequency graph and be ready to write down marks next to each frequency. Now, keeping the level the same, play a 20Hz tone or the lowest you can with your predestined settings. Note the dB level on the meter and write it in on the frequency chart. Go to the next tone on the CD which is probably 25Hz or so. Note that dB level and write it down as well. Go through ALL of the frequencies until nothing registers on the meter. When you’re done, you’ll have the response of the driver. You can even make marks at the appropriate level and connect the dots to see the actual graph plot line if you like. We’re ½ done already!
Now we need to find out how the same enclosure does in the vehicle. Put the sub enclosure in the vehicle in the orientation that it will be installed. Now here is the tricky part – where to put the mic… Do you want to measure it at your approximate face location, on top of the dash or what? If you put it at your face location, it will be different for the passenger. I typically measure from the center of the vehicle. Now, on another frequency graph, go through the same steps again. When you’re done, you can derive the TF for your vehicle!
Simply subtract the “free-air” db level from the in-vehicle level and note the difference. I like to take a 3rd frequency graph and refer to the middle horizontal as 0dB. If your difference at 20Hz is +12dB, mark that on the 3rd graph. As you go higher in frequency, the gain will reduce until you get out of the subbass region. Then it will bounce up and down for the rest of the octaves. Another way to do it is to write down all of the test tones you have on your CD on a piece of paper and then write the +dB or –dB amount next to each frequency.
That’s it! Now you know the TF of your ride. From this point on, any speakers you put into your box will be affected in the same manner.
Piece of cake!
Now let’s look at Boundary Loading, Soundwaves and how important placement and aiming a subwoofer enclosure is…
Boundary loading specifically has to do with soundwaves being reinforced by reflecting off of surfaces. If a woofer were suspended from a hanger in the middle of a room, it is playing into “full space”. By simply mounting it in a wall and firing into a room, the woofer only has to excite the air in front of the woofer, nothing behind it. Cutting this in half if called “1/2 space loading (go figure…) The 3dB rule states that if we double our woofers or power, we will gain 3dB. In similar respect, by half space loading, we theoretically have “double the energy” in the excitable area. Now, if we take that woofer and slide it to the floor, we now got rid of the need for the woofer to excite any air below it. This has cut the excitable area in half again. Not surprisingly, this is called “1/4 space” loading and yields another 3dB. Again, slide to woofer to one side again the perpendicular wall. Now we cut the area in half yet again because we do not need to excite the air behind, below or to one side of the driver. What’s this called? Yup, “1/8 space” loading for another 3dB. Does this always work 100% of the time? Unfortunately not. In most home audio/theater systems, the subwoofer is always placed in a corner for just this reason. In a car, we have many more things to deal with. Mother Nature takes her effect with axial mode and complex oblique mode reflections and resonant frequencies which screw things up at times, but don’t worry, I am not going there! :^)
Many people think that the best place for an enclosure (in a sedan) is in the trunk towards the front end facing backwards. Let’s see how this compare to facing forwards as well as facing backwards and forwards with the box at the back of the trunk by the bumper…
In the graphs below, the vertical black line represents the back of the car. The horizontal line represents the length of the vehicle. The red line represents the incident or “direct” soundwave coming of the cone. Notice that it goes both forwards and backwards. This is accurate because soundwaves do not just go straight forward, but rather in all directions, especially as the frequency drops. The yellow line represents the reflected or “indirect” soundwave after it has bounced off of a surface. The phenomenon of soundwaves being reinforced and getting louder as they “bounce” off of surfaces is Boundary Loading.
In this first graph, the box is facing forward and is up against the back seat. You can see that the indirect wave is doing the opposite of what the direct wave is doing. This will cause cancellation and reinforcement allowing some frequencies to be hard to hear and others to be very pronounced. The indirect wave is also out of phase with the direct wave which will sound “blurry” and not well-defined. This will also sound better if the trunk were open to relieve the cancellation. Dumb – never install a box this way…
This second graph shows the box in the same location but with the woofers facing backwards. This is the most common way sub enclosures are installed… Notice that the indirect wave has improved and it not the total opposite of the first graph. Bass response will be greatly improved. But due to still having some cancellation, the bass will sound slightly better with the trunk open.
The third graph shows the enclosure moved to the back of the trunk by the bumper and facing forward. This yields even better bass and with no improvement by opening the trunk.
The final graph shows the box facing backwards, but still in the back of the trunk by the bumper. The position allows the direct and indirect waves to be nearly in perfect phase with each other! The bass will sound at its best! Taut, clear and “quick”! Ironically, if you open the trunk, you will actually lose bass output. Is that what we all want anyway – strong clear bass that isn’t “muddy” and that doesn’t need the trunk open to get louder?!
So, why don’t people install their enclosures facing backwards at the back side of their trunk? I suppose because it would be hard to set things over the box into the available front area of the trunk. The only downfall I see to having the enclosure in the best possible position (4th graph) is that you may or may not lose a tiny bit of bass due to the lack of boundary loading off of the rear of the vehicle. Regardless, take a moment to set your subwoofer enclosure in the 2 different locations and orientations to experiment for yourself.
