Robert L. Clark of Duke University's Pratt School of Engineering explains.
Just for the record, feedback is actually the mechanism used to control almost every electronic device manufactured. Stability is a critical issue for all of these feedback control systems, and the gain, or level of amplification, used is a critical element in their design. When musicians talk about feedback, however, the connotation is negative because it is the term they use to describe the shreek that results when the gain is too high on the output of an amplified instrument or microphone. There are several potential mechanisms by which feedback can occur when sound is amplified. Let¿s deal first with the simple case of a microphone and an amplified speaker. (See the figure, but ignore the guitar for now.) Feedback occurs when a "loop" between an input and output is closed. In this scenario, the microphone serves as the input and the amplified speaker provides the output.
In our example, the loop between the input and output closes when the sound radiated from the amplified speaker reaches the microphone and is subsequently amplified again. In effect, the cat is chasing its tail. (See the dashed red line connecting the loudspeaker to the microphone through acoustic feedback in the figure.) Gain is an important factor in this instance; it also explains why equalizers are frequently employed to control acoustic feedback. The equalizer is inserted into the "loop" so that one can adjust the amplification of the signal to reduce the troublesome gain. This excessive gain at a particular frequency arises from many factors, including the distance between the microphone and the speaker, the directional nature of the microphone and speaker, the influence of reflective surfaces within the acoustic environment and the presence of additional microphones and amplified speakers.
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Unlike microphones, guitars (both acoustic and electric) can vibrate and these vibrations occur at particular frequencies. In fact, the structural vibrations of an acoustic guitar and the acoustic resonances of the guitar enclosure are coupled and serve to "color" the sound of the guitar. These harmonics are what distinguish the sound of a particular guitar. The top surface of more expensive acoustic guitars is typically made from solid woods such as sitka spruce, whereas less expensive guitars are frequently constructed from laminated wood. The surface vibrations of laminate guitars die out more quickly than those of solid surface guitars.
When a microphone is used to amplify the output of an acoustic guitar, the amplified speaker closes the loop between the input and output when the radiated sound from the speaker reaches the guitar. (See the dashed green line in the figure.) At this point, the sound can further enhance the vibrations of the guitar. If the gain is excessive, this enhancement results in instability dubbed "feedback" by the musician. In such cases, the guitar starts vibrating excessively at a particular frequency and this vibration produces an audible tone. For guitars, this typically occurs at lower frequencies, ranging between 100 and 200 Hz, and results in a "hum."
A similar mechanism occurs when amplifying the output of an electric guitar. Structural vibrations induced by acoustic feedback can magnify the signal generated by the sensors embedded in the guitar to "pick up" its sound, which leads to instability. Equalization can control feedback by reducing the gain at the frequency at which this problem occurs. One must take care in setting the equalization so as not to eliminate the natural harmonics of the instrument over a desired frequency range, however.
My colleagues and I are working to employ smart materials and control approaches that minimize the effects of acoustic feedback on instruments. Currently, the best control approach is to amplify the instruments at a volume that is appropriate to the space. Irrespective of the insertion of equalizing systems or active control strategies, there will always be a gain or volume at which the system goes unstable.
Answer originally published September 15, 2003.