Phase is really tough to talk about.

One reason is, we’ve confused the words “polarity” and “phase” for decades.

The polarity of a speaker refers to the (+) and (-) terminals. If you connect them to the (+) and (-) wires, respectively, you have observed proper polarity.

Let’s assume we have two identical subwoofers, in the same enclosure, close to each other on the same side of the enclosure, sharing a baffle. For the sake of simplicity, let’s assume they are single voice coil woofers.

If they are connected observing proper polarity, both cones will move outward when the amp’s voltage swings positive, and both cones will pull inward when the voltage swings negative.

If you accidentally connect one woofer’s voice coil backwards, so that its cone pulls inward when the voltage swings positive, and pushes outward when the voltage swings positive, you now have two woofers which are fighting each other.

Both are trying to create air-pressure changes, but the work one is doing cancels out the work the other is doing. Because they are close to each other and on the same baffle, and because the distance they are separated is nearly nothing compared to the wavelengths they are playing, almost complete cancellation occurs.

And this is a pretty common error made in car audio. Almost everyone has had this experience. We can relate.

This is an important time to define wavelengths. Here is our friend the sine wave.  If this wave is describing sound in air, the term wavelength refers to the distance between the peaks, one complete cycle. Starting at zero degrees, you can see the progression to 360 degrees.

Now, lets think about two sine waves. These are aligned in phase.

If we sum them together, we get one bigger sine wave, at the same frequency.

Here are two sines, at the same frequency, but 90 degrees out of phase.

If we add two sines that are not quite aligned, the result won’t be as large in amplitude as we would expect from adding two sines which are in phase. That is a form of distortion, if you think about it.

Here are two sines 180 degrees out of phase with each other.

This causes complete cancellation. OK, this takes us back to our hooking up speakers backwards.

When we swap the (+) and (-) wires, we invert the phase 180 degrees. Instead of pushing the woofer cone out, we are pulling it in.

Smaller deviations in phase – less than 180 – don’t result in such a complete cancellation. The cancellation may be near complete, or with smaller errors, it may simply prevent the two signals from adding together to be as loud as they could be. You might lose a lot of energy, or you might lose a little, but you lose some.

This is fundamentally why single-driver speaker systems seem to be relatively insensitive to phase inversion. Some people can hear the difference when you flip polarity, but there is no scientific consensus on which is correct. For the purposes of this article, we don’t care about “absolute phase” – we only care about phase interactions.

Now, if you think about it for a moment, the odds of two subwoofers being connected opposite-polarity of each other is about the same as the left and right side front speakers accidentally being connected opposite-polarity of each other. But we probably don’t remember this experience nearly as often. Why?

Well, one reason is, with deck replacements, the harnesses are color-coded and it’s literally harder to make that mistake than it is with most larger clear-jacket speaker wire.

But there are two more complex reasons at work also.

When two speakers play the same note, the possibility of the two speakers’ output interfering with each other and causing cancellations always exists.

Crossovers. A high-pass speaker (say, a tweeter) and a low-pass speaker (say, a midrange) will play the same notes in the transition band of the crossover – the band of notes where the output overlaps as the crossover filter begins to do its attenuation. The output of these two frequency-adjacent speakers can cancel each other because of the crossover filters we have chosen. 12dB Butterworth, for example, probably the most common crossover filters used historically, put the speakers 180 degrees out of phase with each other the crossover point –  in the electrical domain!

If both speakers are the same distance from us, and they are connected observing the proper polarity, they now are cancelling each other out simply because of the crossover filter we selected! So, experienced speaker designers simply flip polarity of one driver, and the problem is solved. Alternately, you can select crossover filter types which don’t have this problem (24dB/octave Linkwitz-Riley filters are often used for this reason).

Path-Length Difference. If the two speakers are connected observing proper polarity, and they are the same distance from us, and they are sent the same content to play, they are in phase with each other. But what if the two speakers are different distances from the listener? The difference in the length of the paths the sound travels will put the two speakers out of phase at certain frequencies.

With the subwoofer example above, the wavelength at 80 Hz is about 166 inches.  That’s the distance a wave takes to go from 0 degrees, all the way to 180, and then back to 0 (in a circle, 360 degrees = 0 degrees). That means that half a wavelength is 83 inches – halfway through, the wave is at 180 degrees opposite where it started. That means that if the two speakers are 166 inches apart, they will be back in phase with each other. If the speakers are only 83 inches apart, they will be 180 degrees out of phase with each other. If they are 249 inches apart, they will again be 180 degrees out of phase with each other.

So, if the two subwoofers are connected properly, but one sub is 83 inches farther away than the other sub, there is a big cancellation at 80 Hz. Fortunately, this doesn’t happen in cars because they aren’t big enough. Even if we put the two subwoofers on opposite sides of the trunk, they aren’t far enough apart to create significant distance-related cancellation.

However, the wavelength of sound at 125 Hz is only about 108 inches. Half a wavelength becomes 54 inches. That rough amount of “path-length difference” happens fairly often in a car, in two situations:

• The trunk subwoofer and the door midbass are often very far apart. That is why getting those speakers in phase with each other can be so tricky.
• There are rear speakers playing as loudly as the front speakers.

The wavelength of sound at 250 Hz is about 54 inches. Half of that is 27 inches, and that’s a pretty common “path length difference” between the left and right doors from a listener’s perspective. A left speaker and a right speaker are playing the same range of notes in a stereo system. Any content present in both the left channel and right channel, at similar amplitudes,  will be played by both the left and the right speakers, at similar loudnesses. That means that if your left door speaker and right door speaker have a “path-length difference” of 27 inches, they will be 180 degrees out of phase with each other at 250 Hz. That’s a pretty common problem in car audio – getting cancellations starting at around 250 hz. (Note that this won’t affect left-only or right-only content).

The wavelength of a 3000-cycle wave is about 4-1/2 inches. So if the two speakers have a path-length difference 4.5 inches, they will be back in phase with each other. If the speakers have path lengths differing by 2.25 inches, they will be 180 degrees out of phase with each other. If they have 6.75 inches of path-length difference, they will be back to 180 degrees out of phase with each other.  When can that happen? When we have midranges and tweeters slightly separated from each other, or midbass and midrange speakers. If the two speakers are adjacent speakers driven by high-pass and low-pass portions of a crossover filter network, say mids and tweeters, they will overlap in the transition band, as mentioned above.

When the path-length difference is 1/2 the wavelength of the crossover frequency, the speakers will be 180 degrees out of phase at that frequency, which is in the center of the transition band.

Also – and stick with me for a moment – if the path-length difference is an odd multiple of 1/2 the wavelength of the crossover frequency, the speakers will be 180 degrees out of phase. At one-half a wavelength, you’re 180 out. At one full wavelength, you’re back in. At one-and one half wavelength – or 3 halves – you’re back out of phase. At two wavelengths – or four halves – you’re back in phase.

You do not have to remember all that! Almost all DSPs will do that math for you – you enter the distance to each speaker, and the software does the calculation. The few that don’t do the calculation allow you to enter a raw path-length difference in inches or centimeters (even if they don’t tell you that’s what you’re entering). You can calculate path-length differences by using subtraction on a piece of scrap paper.

When we select crossover filters, we are doing the job of a speaker designer. When we use delays, we are making up for the limitations of the car cabin. In either case, we are managing phase cancellations – even if we didn’t realize it!

The reason we haven’t noticed speakers accidentally being opposite-polarity as often as we have subwoofers is that the cancellations aren’t complete – they don’t cause near-complete silence, the way two out-of-polarity subwoofers do! There’s enough phase cancellation in “normal” door speakers (i.e., in systems not using delay) that it doesn’t sound perfect either way, and it’s harder to tell the difference.

Now, delay only works for one listening position. There are other ways to manage phase (all-pass filters being one). But we can’t start to use them until we understand the objective. Understanding this allows us to use what the OEM has done to partially manage phase – and improve upon it – without wasting a bunch of time.