Why does helium make your voice squeeky?
While this question has been answered ad nauseam, most answers contain an error or wave their hands at some point. Here is my attempt at a complete, compact explanation.
The speed of sound $c$ in a gas depends on the gas’ temperature $T$ and molecular mass $m$, but not the gas’ density or pressure (where $N_A$ is Avagadro’s number and $k_B$ is Botzmann’s constant)$$c = \sqrt{\frac{N_Ak_B T}{m}}$$This is because temperature controls the “average kinetic energy per particle”, and kinetic energy translates to velocity as the square root. Since helium has a mass about 7 times smaller than nitrogen or oxygen, at standard temperature and pressure sound travels $\sqrt{7}\approx3$ times faster in helium versus air.
The wavelength of sounds changes when your helium voice leaves your mouth, at the helium-air interface. However, the frequency does not change, so the higher pitch is not a result of the gas interface. Voices still sound squeeky in a helium filled room, which makes saturation divers sound rather silly.
The vocal chords don’t vibrate substantially differently in helium. In fact, vocal chords don’t sound like your voice. Vocal chords flap together like a trumpet player’s lips in their mouthpiece, creating a raspy tone.
Like most instruments, your voice acquires its full sound via your resonant chamber. The impulse of the vocal chords rings up and down frequency to create harmonics that sound like your voice. The effective size of your resonant chamber is the origin of the pitch change! The fundamental frequency of a resonant chamber of size $L$ is the number of times a sound wave can richochet per second$$f_0\propto\frac{c}{L}$$Changing $c$ while maintaining $L$ creates a different resonant frequency $f_0$. Since $L$ is unchanged when we breathe Helium, but $c$ increases nearly three times, our Helium voice is almost two octaves up (since an octave doubles frequency).
To summarize, changing the speed of sound of a gas is like changing the size of one’s voice instrument. Faster sound waves see a small instrument (helium turns a flute into a picolo) and slower sound waves see a large instrument (nitrous oxide turns an oboe into a bassoon). This can be demonstrated rather dramatically by playing a trumpet filled with helium.
Examples of hand-waving
I wrote this blog because the top results on Google are wrong or misleading. Many articles try to convince one that helium voice isn’t actually higher pitched, which defies my lived experience. Here are a collection of misleading explanations.
This article ignores the effective size of the resonant chamber in favor or “responsiveness”
Some people think that the helium changes the pitch of your voice. In reality, however, your vocal cords vibrate at the same frequency. The helium actually affects the sound quality of your voice (its tone or timbre) by allowing sound to travel faster and thus change the resonances of your vocal tract by making it more responsive to high-frequency sounds.
This Action Lab video correctly introduces the resonant chamber and demonstrates it getting squeakier with helium. This is correctly explained as “timbre” — a change in the sounds produced by the resonant chamber. But then the Action Lab claims that while your voice “sounds” higher, it isn’t actually at a different frequency. What?!
While the fundamental vocal chord frequency may not change with helium, the full human “voice” is a wideband signal dressed in resonances (called “formants”). A human voice is not one frequency; when I sing into a spectrogram, I see four octaves of resonance above the note I am singing. Helium voice sounds squeaky because this four-octaves of resonant dressing is up-shifted by nearly two octaves. Thus, helium voice contains less low frequency sound and the mean vocal frequency is shifted higher. Helium voice sounds higher frequency because it is higher frequency, even if the primary impulse frequency of the vocal chords doesn’t dramatically shift.
The false claim that “timbre” doesn’t effect the perceived pitch of your voice is everywhere!
Rather the timbre, or quality, of the sound changes in helium: listen closely next time and you will notice that a voice doesn’t become squeaky but instead sounds more like Donald Duck.
When I listen closely to helium voice I hear is a higher-pitched voice. The loudest (primary) pitch may not have changed, but that one frequency sits atop a wideband resonant pedestal that dramatically increases its frequency. Helium voice sounds higher-pitched and squeakier; enough with this gas-lighting!