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I do not know much about the anatomy of the vocal chords, but if we can(2)
assume that their sizes are fixed and in first approximation do not
depend on muscular effort, then each cord (more accurately, corresponding
resonating cavity?) must produce a system of standing waves of fixed
lengths regardless of surroundings. The frequency of the produced sound,
however, should depend on its speed. Since the helium atoms are lighter
than the air molecules, the speed of sound in helium, at the same
pressure and temperature, is greater than in air. Hence the higher pitch.
So I would not expect the change in spectral composition of the produced(3)
sound, rather the whole hierarchy of the fundamental frequency and its
harmonics shift up in the same proportion.
If this is true, the same effect should be observed in air under higher(4)
pressure.
I do remember vaguely, as a schoolgrader, reading stories to that effect
about deep underwater experiments, but what is stuck in my memory, is only
mentioning that people working deep underwater (under accordingly higher
air pressure in the chamber) hear their own and others' voices sounding
weird. Maybe, someone in contact with those working underwater have more
detailed information about this effect.
Moses Fayngold,
Physics Department, NJIT