The Helium "Donald Duck" Effect

The human voice originates when the stream of air flowing up the trachea undergoes pressure modulations as it passes between the vibrating vocal chords in the larynx. The sound produced consists of a fundamental frequency, which determines the voice's pitch, and harmonics (integral multiples) of this frequency. For adult males and females the average frequencies of the fundamentals are 130 hertz and 205 hertz, respectively. The amplitudes of the harmonics for vowel sounds vary approximately as the inverse of the 1.5 power of the order of the harmonic.

The sound that exits the mouth is the result of selective transmission by the configuration of the vocal tract (throat, mouth, and nasal cavities) produced by the tongue and lip constrictions. For any cavity, sound waves bouncing back and forth within it will interfere constructively for certain frequencies (the resonance frequencies) to produce a loud sound. The cavities in the vocal tract have such resonances, and the maxima in the sound transmission curve correspond to the resonance frequencies. Those harmonics near a resonance frequency of the vocal tract will be strongly transmitted, while the other harmonics will be damped. The lowest-frequency peak in the transmission curve is referred to as the fundamental, while the regions at the other peaks are called formants.

The fundamental frequency of a resonating cavity is directly proportional to the speed of sound in the gas occupying the cavity. But from the kinetic theory of gases, as well as direct measurements, we know that the speed of sound in an ideal gas (such as dry air) is proportional to the square root of the ratio T/M, where T is the absolute temperature of the gas and M is its molecular weight. For a fixed temperature and cavity volume, it is clear, therefore, that the speed of sound will be greatest for gases with the smallest molecular weights. For example, the speed of sound in dry air (M=28.964) at 0 degrees Celsius is 331.3 m/s. At this temperature in helium (M=4.003) the speed is 891.2 m/s. The resonance frequencies of the vocal tract, and hence the formants, are therefore almost 2.7 times higher for helium than for air. At a pressure of one atmosphere, with pure helium in your vocal tract instead of air, the pitch of your voice will be about two and a half octaves higher than usual (like Donald Duck's). For a helium-oxygen mixture containing 68% helium by volume, the pitch increase is only one and a half octaves.

E. G. Richardson, "Technical Aspects of Sound" (Elsevier, New York, 1953), Chapter 10.

F. Reif, "Fundamentals of statistical and thermal physics" (McGraw-Hill, New York), Chapter 5.