John Smith, a physicist at the University of New South Wales in Sydney, Australia, belts out an answer to this query.

In both speech and singing, we produce sustained vowel sounds by using vibrations of our vocal folds—small flaps of mucous membrane in our voice box (or Adams apple)—that periodically interrupt the airflow from the lungs. The folds vibrate at a fundamental frequency, fo, which determines the pitch of the sound. In normal speech fo is typically between 100 to 220 hertz (Hz), or vibrations per second. In contrast, a soprano's fundamental frequency ranges anywhere from 250 to 1,500 Hz. Speech and singing also contain a series of harmonics—which are basically multiples of the frequency in question—with frequencies of 2fo, 3fo, 4fo, and so on.

Usually, the fundamental frequency has the greatest acoustic power, but the very high harmonics, although less powerful, have the advantage of residing in a range above about 3,000 Hz, where the orchestral accompaniment provides less competition. Sopranos have an advantage over lower voices, such as the bass and tenor: Due to their higher range, the auditory frequency at which they sing, as represented by their fo, lies in the neighborhood of frequencies to which the ear is most sensitive. In contrast, the lower fundamental frequencies of male voices cannot compete as easily with the power of an orchestra; male singers, therefore, must often rely on their higher harmonics in order to be heard.

Classically trained sopranos also make use of a technique called "resonance tuning" to intensify the vibrations of the vocal folds and increase the power of the voice. The vocal tract—the "pipe" between the voice box and the mouth—has a series of resonance frequencies: R1, R2, R3, et cetera. Harmonics that fall at or near these resonance frequencies are most efficiently radiated as sound.

The two lowest frequency resonances, R1 (approximately 300 to 900 Hz) and R2 (approximately 800 to 3,000 Hz), play an important role in speech, providing high power for harmonics of fundamental frequencies that are close to them. Further, we can vary resonance frequencies by moving our tongue, lips, jaw, and so on. Thus, adjusting the configuration of the mouth alters R1 and R2, and this in turn changes which harmonics are emphasized.

In singing, the fundamental frequency determines the pitch, which is specified by the composer or performer. Singers can significantly increase their loudness by adjusting the resonance frequencies of their vocal tract to closely match the fundamental frequency or harmonics of the pitch. Sopranos can sing with fundamental frequencies that considerably exceed the values of R1 for normal speech, but if they left R1 unaltered, they would receive little benefit from this resonance. Consequently they tune R1 above its value in normal speech to match fo and thus maintain volume and homogeneity of tone. This is often achieved by opening their mouth wide as if smiling or yawning for high notes, which helps the tract act somewhat like a megaphone. (This tuning of R1 away from its values in normal speech, as well as the large spacing between harmonics, has implications for intelligibility, and is one reason why singers can be hard to understand at very high pitch.) Singers at lower pitch sometimes tune R1 to match harmonics (for example, 2fo) rather than the fundamental, but do not usually practice resonance tuning as consistently as sopranos.

Although singers can generate very loud sounds, how can they compete with a large and enthusiastic symphony orchestra?

One strategy is to maximize their sound output at frequencies above 2,000 Hz. This is because an orchestra is typically loudest around 500 Hz, with the sound level dropping off quickly at higher frequencies. Furthermore, the ear is most sensitive around 3,000 to 4,000 Hz. To this end, singers often modify the resonances of their tract to produce a characteristic "vocal ring" that considerably boosts the sound output in this frequency range. This is of more value to lower pitched voices than to sopranos.