This article is from the Acoustics FAQ, by Andrew Silverman with numerous contributions by others.
Many people, on hearing the voice of someone who has breathed helium, believe that the person's speech pitch has increased.
WARNING - Breathing helium can be very dangerous.
A cavity will have certain resonant frequencies. These frequencies depend on the shape and size of the cavity and on the velocity of sound within the cavity. Human vocal cords vibrate non-sinusoidally in the vocal tract, giving rise to a range of frequencies above the fundamental. The vocal tract mainly enhances lower frequency components imparting the recognizable voice spectrum.
The velocity of sound in helium is much greater than in air, so breathing helium will raise the vocal tract's resonant frequencies. Although the vocal cords' vibrational frequencies are little affected by helium, the effect of higher cavity resonances is to alter substantially the relative amplitudes of the voice spectrum components thus leading to apparent pitch change.
 
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