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Why does your voice sound squeaky when you talk after breathing in helium?

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Wrong answers This is an interesting question, which is often answered wrongly. The usual wrong answers are something like one of these:
  1. The speed of sound is faster in helium than air, so ...
    • the sound has a higher frequency.
    • the sound waves bunch up when they pass from helium to air, giving them a shorter wavelength which makes them sound higher.
  2. Your vocal folds vibrate faster in helium than air, because helium is lighter than air so provides less resistance to the movement of the folds.

From a physical point of view, explanation 1 is nonsense. It's true that sound travels faster in helium. However, if your vocal folds vibrate at a particular frequency, say 100 times a second, there will still be 100 pulses a second reaching your friend's ear, no matter how fast they travel or through what changes of medium. This frequency is what we perceive as pitch.
There is a very small grain of truth in explanation 2. However, the main resistance to movement of the vocal folds comes from their own mass (inertia), tension, connection to surrounding tissue, etc. Compared to these, the retarding effect of air resistance is negligible, and the effect of reducing it is imperceptible.
 Right answer The above taken together suggest that breathing in helium does not change the pitch of your voice. This is in fact correct: helium speech is not higher in pitch than normal speech. So why does it sound "squeaky"?
The answer is that the higher speed of sound in helium changes the resonances of your vocal tract. In particular, the formants or resonant frequencies are higher. These formants affect the timbre of your voice, as well as what vowel people hear. It's the change in timbre that people notice in helium voice. This sometimes makes them mistakenly think the pitch of the voice is higher.
 A bit more detail When your vocal folds vibrate, they produce waves at the vibration frequency (f say), as well as at all higher multiples of that frequency (2×f, 3×f, etc). Completely independently, the vocal tract has certain resonant frequencies depending on its shape and size (and the speed of sound). Partials (multiples of f) near the resonant frequencies are amplified, and other multiples damped, when the sound wave passes through the vocal tract. You can change these resonant frequencies by moving your tongue and lips - which is how you make different vowel sounds.
The higher speed of sound in helium makes the formant frequencies higher, so the partials that are amplified are higher with helium in the vocal tract than with air. This causes the distinctive change of timbre (and also makes it harder to distinguish different vowels).
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Why is my voice squeaky?

Voice is created by air being pushed from the lungs through your larynx, aka voicebox, and then resonance is altered by other parts of your head that move and or vibrate (mout