Understanding Relationships: Bringing Clarity To Phase, Frequency And Time

The resultant effect of loudspeakers that are offset from one another is the often mentioned “comb filter” response pattern.

The term comes from the hundreds of additions and subtractions that corrupt the frequency and phase response of the system, which end up resembling the teeth of a comb.

Here’s an example of how phase-offset manifests in the real world: a 600 Hz wavelength is 1.5 feet long (18 inches), whereas a 6 kHz wavelength is just 0.15 feet in length (1.8 inches).

Therefore, if one loudspeaker is offset in relation to another loudspeaker by 0.15 feet, a signal at 6 kHz will cause the two sources to totally cancel each other - at least in theory.

In reality, however, total cancellation is actually unlikely, due to the imprecision of most loudspeakers. Nonetheless, a large percentage of cancellation – possibly as much as 90 percent – will inevitably occur.

But move upwards, let’s say to 6.5 kHz, or downward to 5.8 kHz, and the whole picture changes. That’s because acoustical addition and acoustical cancellation will always be a function of the wavelength of the source material in relation to the physical and/or the electrical offset that’s affecting the relevant signals.

Conversely, the same offset of 0.15 inches represents only 1/10th (0.1) of a phase differential of the 600 Hz wavelength. By no means is this desirable, but it’s not going to cause much more than about a 10 percent cancellation of forward radiated energy. (It will also change the polar response of the system, but that’s another topic for another time.)

This is precisely why we speak of – and why we measure – the phase relationship of multiple sound sources, instead of thinking only about the pure time differential. A phase-versus-frequency response measurement will characterize the arrival time of a sonic wavefront at a given point in space, in relation to the wavelength of each relevant frequency.

That may sound difficult so here’s a simplified analogy:  A firing squad of five shoot at the same target at exactly the same time with exactly the same rifles, but each one is standing a few feet behind the other. Therefore, the projectiles do not reach the target at precisely the same time.

While it might not mean much, insofar as the ultimate intent of the firing squad, it means absolutely everything when a “sound squad” wants all of the sonic energy from each loudspeaker in the sound system to arrive at the listener’s position in perfect phase with all the other loudspeakers.

Unlike rifles, if the sonic energy doesn’t arrive at exactly the same time from all sources, cancellations and additions will occur, causing an imperfect and comprised frequency and phase response.

Phase & Polarity

We often hear phase spoken about in a very basic manner, such as “one loudspeaker is either ‘in-phase’ or ‘out-of-phase’ with another.” This is more correctly referred to as the polarity relationship of the loudspeakers. When polarity is reversed, then all of the energy emanating from a loudspeaker – without respect to frequency – is also reversed.

In such a case, two theoretically perfect loudspeakers would perfectly cancel each other’s entire output across the full audible spectrum. However, this won’t actually occur due to the physical imperfection of virtually all known loudspeakers.

What does in fact occur is that the low frequencies will almost totally cancel each other because the physical imperfections of the loudspeakers are relatively minor in relation to the long (and therefore forgiving) LF wavelengths, while the shorter wavelengths of the high frequencies will partially cancel and partially combine, causing havoc with the MF and HF frequency and phase response.

It’s worth noting that a phase offset of multiple sound sources is akin to how a flanger works. The effect of “flanging” was originally created by slowing down a reel of tape on a tape recorder that started out in sync with another tape recorder playing an identical track.

Flanging was accomplished by applying your finger on the edge of the reel to alter the speed of the tape machine (hence the term). The small offset in time created the well-known sonic effect that’s now easily replicated by the use of modern analog and digital electronics.

But it’s also important to note that a flanger is an intended sonic effect.

Source: Live Sound International

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