Inhaling helium (which is not recommended) does not actually increase the pitch of your voice. The timbre of your voice changes so you sound squeaky, which is interpreted as higher in pitch.
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Key Facts In This Video
Sound is caused by vibrations traveling through the air. 00:26
Helium's speed of sound is 3 times faster than the speed of sound in the atmosphere. 01:13
Inhaling helium doesn't affect the volume or pitch of one's voice, only the timbre. 01:35