# does audio feedback consist of harmonic content?

So sound from musical instruments as well as human voice consists of harmonics. just wondering if feedback from speakers also have harmonics component I have heard that feedback does not consist of harmonics, whereas from other sources, it says that it consists only odd harmonic frequency content. so which is true?

• The speakers may also introduce some harmonics/distortion. It's not a perfect linear device. The louder its playing the more non-linear it gets. I assume that you talk about acoustic feedback. – niaren Aug 23 '19 at 6:30

Audio feedback happens when the loop gain from the microphone to the speaker and back to the microphone is larger than 1 (ignoring some other phase considerations that in practice rarely matter).

At this point a single frequency starts building up and gets louder and louder. Theoretically it would get infinitely loud, but obviously that can't happen in the real world.

In practice to are limited by some system constraint: could be a real limiter kicking in, amplifier clipping, power supply sag, driver out of excursion, microphone clipping, protection circuit or algorithm, etc.

The harmonic structure is mainly determined by the specific nature of the system constraint(s). A well designed limiter would keep this pretty close to a pure sine wave, amplifier clipping will generate lots of harmonics. Odd harmonics are more likely than even ones, but you can certainly get them both.

The contradicting statements may be a result of looking at two different aspects of the situation. As Hilmar pointed out in an earlier answer, any clipping (be it electronic or mechanical) will indeed produce harmonics.

However, feedback distortion (not necessarily reaching to the point of the loud feedback oscillation being produced) definitely does not consist of harmonics, or even any spurious frequencies added! Feedback distortion comes from a frequency response with a very weird structure (very unnatural to the ear, often described as adding a metallic quality to the original sound).

The reason is the following: since the sound takes a fixed amount of time to travel from the speaker to the microphones (simplified analysis assuming single speaker and single microphone, no echos/reflections, and no attenuation of sound w.r.t. distance traveled), then the frequencies at which the feedback is positive, thus producing peaks in the frequency response, are the frequencies $$f$$ such that $$d = k \frac{\,c\,}{f}$$ where $$d$$ is the distance between the speaker and the microphone, $$c$$ is the speed of sound, and $$k$$ is a positive integer. In other words, positive feedback (and thus larger gain) occurs at frequencies where the distance between the speaker and microphone is an exact multiple of the corresponding wavelength.

Now, you see, that means positive feedback occurs at frequencies $$f_k = k \frac{\,c\,}{d}~~~~k = 1, 2, 3, \cdots$$

There, you can see that the distortion is not harmonic in nature --- first of all, the above, assuming gains are low enough that you don't produce clipping or oscillation, is linear distortion (strangely enough, seeing how the feedback distortion is a very unnatural-sounding artifact); and second, the spectral locations of the "spurious" frequencies are fixed and equi-spaced, independent of the input frequency. In fact, harmonic distortion applies to an input tone (a sinusoid at a fixed frequency), whereas feedback distortion simply introduces a "weird/unnatural" frequency response, so it applies to signals with a spectrum covering ranges of frequencies.

A feedback oscillation may be subject to a combination of both effects: it may still carry a perfectly audible "feedback distortion" quality (especially if the gain is just enough to produce the oscillation), while it may or may not produce clipping that adds harmonic distortion to the mix.