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Acoustic Resonance Details

Standing Waves

A standing wave is a wave with a fixed position. Whereas a sound wave propagates through space, a standing wave sits where it is. In the case of voice, a standing wave is created by the interference of two waves moving in opposite directions, as in this animation (courtesy of wikipedia).

The two waves in our case are the incident wave, the sound wave being produced by the vocal folds, and the reflected wave, which is created when the initial wave arrives at the exit of the vocal tract, and a portion of it is reflected back towards the glottis by the changing medium.

Nodes and Antinodes

In a standing wave, the points at which amplitude is at a minimum are called nodes, and the points at which amplitude is at a maximum are anti-nodes. In the context of voice, the amplitude we are referring to is as a measure of pressure, and of volume velocity. A pressure node (where pressure is at a minimum) will denote a volume velocity anti-node, and vise versa. In the vocal tract, there will always be a pressure node at the exit (where the greatest movement of air is possible), and a pressure anti-node at the glottis.

Interference

When a sound wave travels through the vocal tract and meets its reflection (and therefore, the standing wave that the two are creating), it may be dampened or maintained depending on its characteristics. If the wavelength of a sound wave roughly matches the characteristics of the vocal tract with maximum volume velocity as it reaches the exit, it will be reinforced. The lowest frequency with such a wavelength is the first resonance frequency, which will have a wavelength four times the length of the vocal tract. The next lowest frequency will be the second resonance frequency, with a wavelength 3/4 the length of the vocal tract, and an additional node/anti-node pair, the former in the oropharynx, the latter in the anterior oral cavity.

Perturbation

So far we have only discussed resonance as it is affected by the length of the vocal tract. While this is fine for a simple tube with equal diameter throughout its length, that is clearly not what the vocal tract is, and as discussed earlier on this page, resonance frequencies are affected by more than just length. A perturbation or constriction at or near a pressure anti-node will raise the frequency of the corresponding resonance, while a constriction at a pressure node will lower it. All resonance frequencies will therefore be raised and lowered respectively by constrictions at the glottis and lips. The second resonance frequency will be raised by a constriction in the front of the oral cavity (as in the vowel /i/), and lowered by constriction in the posterior oral cavity/oropharynx (as in the vowel /u/). As we examine progressively higher resonance frequencies, the number of nodes and anti-nodes increases, making it increasingly difficult to isolate them. This is why you will rarely see anyone discuss anything higher than R3/F3.