This question (and answer) is an attempt to clear the air on what appears to be a very simple issue, with conflicting or unclear explanations on the internet. Arguments, negations, etc are invited.

I'm classifying this as a physics question, since it has to do with resonances, attenuation, etc.

Question:
I recently Googled this, and found a ton of articles with confusing explanations:



One of the top Google results from a site called Live"Science", says - "....their wavelengths stay the same regardless of whether the tract is filled with helium gas or air....That means the frequencies of the resonant harmonics must increase in a helium-filled cavity instead."
The above appears to completely contradict the source university article as well as this other article in Scientific American that say the pitch of the sound (and the actual frequency of oscillations) doesn't change, only the timbre (and the distribution of power between low and high frequencies) changes.
Additionally, neither the university article quoted nor Scientific American explain HOW the presence of helium leads to the presence of higher frequencies. For example, the university article simply says - "Inhaling helium changes the frequencies of the resonances, and therefore of the formants they produce" --- Okay, how?
There also appears to no consensus on whether a LISTENER in a helium atmosphere would hear the same frequencies as normal (it's helium all the way so it shouldn't make any difference right?) OR hear the squeaky voices associated with helium. This should be explainable by physics, what is the answer?


In order to properly understand this without any unnecessary "controversy", let's break the whole process of sound generation and perception into 5 important, but completely separate parts. We'll then proceed to explain each part using a few different examples and pieces of derivative logic:


Vibration of the vocal folds
Transmission of energy from vocal folds to air in the vocal tract
Resonance and Attenuation in the vocal tract
Transmission of energy from the end of the vocal tract (mouth) to the surrounding medium
Reception and perception of sound by another human.



Now:

1. The frequency generated by the vocal folds depends on the tension exerted on them and surrounding muscles. This is a neuromuscular process and is NOT affected by Helium or any other gas (at least in the short term). 

So our vocal folds continue to vibrate at the same frequency in helium as in normal air.

2. Sound is produced by the transmission of the vibrations produced in the vocal fold, to the air in the vocal tract. This "transmission" doesn't occur by any magic. The vocal folds - as they vibrate - push and pull columns of air in their immediate vicinity, not very different from the way you may push a child on a swing at specific intervals, so as to produce sustained oscillations, and brief enjoyment. (The "pull" in this analogy though, is provided by gravity). 

The point is, the child oscillates at the same frequency at which you are pushing the swing. i.e. If you are pushing the swing once every N seconds, the child also completes a swing once every N seconds. This is true regardless of the weight of the child, correct?

Similarly, the air in the vocal tract, also vibrates at the same frequency as the vocal chords. This fact, is also true regardless of the mass of the air particles.

In other words, the frequency of sound does not change, regardless of the medium in which it is transmitted.


  Time-Out
  
  The last one was a doozy. Frequency of sound does not change? Then
  why on earth does helium sound different from normal air?
  
  While the frequency of sound does not change, the SPEED of sound does.
  Why? Consider this old classical physics equation:
  
    Kinetic Energy = 0.5 * m * v^2,
  
  where m = mass and v = speed (let's not say 'velocity' for now)
  
  Now the vocal chords, vibrate with the same Force N at the
  same frequency T. Thus the energy it conveys must be the same
  in ALL media.
  
  In other words, for a given constant value of Kinetic Energy, v^2 is
  inversely proportional to the mass of the particles.
  
  This naturally means sound travels faster in Helium than in
  air.
  
  Now, we know the other old equation:
  
  Speed = Wavelength x Frequency
  
  Now since we know that the FREQUENCY of sound is the same in Helium
  and in Air, and the speed of sound is greater in Helium, it follows
  that the Wavelength of sound is greater in Helium than in Air.
  This is a very important conclusion, that bears directly on our next
  deduction.



3. Now, we have a very important conclusion in our kitty - "Wavelength of sound is greater in Helium than in Air".

Remember that the vocal tract is often modelled (simplistically) as an open or closed tube. To refresh why that's important, see Wikipedia.

The vocal tract is actually not really a cylinder, but a fairly complex shape. This means it has areas of constriction and expansion that change depending on the position of your tongue, tension in the tract, and several other factors.

So in a sense, in these complex configurations, the vocal tract can be modelled as  a series of tubes of varying diameters and varying levels of "closure" of either openings. 

Now this means, that different parts of the vocal tract, depending on their geometrical configuration and their material characteristics, resonate with different WAVELENGTHS of sound.

Notice I said WAVELENGTHS and not FREQUENCIES. In common parlance, "Frequencies" is often used since W and F are directly inter-related in a common medium. However, even if we change the medium through which sound is being propagated, the interaction of sound waves with open and closed tubes depends strictly on its wavelength and not its frequency.

Now would be a good point to return to the marquee conclusion we drew from point 2 - "Wavelength of sound is greater in Helium than in Air".


  This leads us to the following KEY/FINAL CONCLUSIONS:
  
  In a vocal tract filled with Helium:
  
  1. The frequencies of sound do not change
  
  2. The wavelengths of sound DO change
  
  3. Because the wavelengths have changed, the portions of the sound spectrum produced by the vocal chords that are attenuated and resonated by different portions of the vocal tract, also change.
  
  4. This results in the sound spectrum output by the combination of the vocal chords and vocal tract in Helium, being different from the sound spectrum output in normal Air.
  
  5. This means, the net distribution of energies among high and low frequencies (or the timbre) changes with a change in sound medium. Whereas the fundamental frequency of the sound (closely related to pitch) does not change.
  
  Let's look at the spectrogram of two sample sounds helpfully provided in the NSW article.
  
  
  
  Unfortunately due to the experimental conditions the two sounds do not have the same content (different sentences are spoken) and therefore the spectrogram cannot be exactly relied upon. However, the fundamental frequency in both is roughly the same and therefore supports our conclusion that the pitch is the same. Since different words are used in either sound, a timbre comparison cannot be made (since the difference in energy distributions visible in the spectrogram can be attributed to the different words spoken).
  
  Also, for simplicity and ease of understanding a "Melodic Spectrogram" has been used in favor of the raw, noisier spectrogram. It was generated using Sonic Visualizer.




We are not Done!

We started with the promise of explaining sound transmission and reception/perception in FIVE parts. We are done with only three. Let's get through the remaining parts very quickly.

4. Transmission of sound from mouth to air - As covered by point 2, with a change in medium, the sound frequency does not change, but the wavelength does. This means that the only effect of filling a room with helium as well (rather than just the vocal tract) is to increase the wavelength of the sound.

5. The above has no impact on sound perception. The ear and brain together are primarily a FREQUENCY receiver. The ear translates air pulsations into hair cell oscillations, which then translate to synchronous pulses on attached neurons. Since the timing of the pulses is correlated ONLY to frequency, and the timing of the pulses is what produces notions of pitch, timbre etc, we can safely assume that the ear transcribes sound to the brain faithfully based on frequency. Wavelength has no impact on this process.

However, the ear, just like the vocal tract, is non-linear. Which means that it too, is going to attenuate/resonate some sounds (the specific non-linear properties of the cochlea are still being studied). However, UNLIKE the vocal tract, the ear/cochlea is a sealed, fluid-filled chamber. The properties of the cochlea are not affected by surrounding air but only by the fluid, which of course could be affected by blood composition and other biological factors. But NOT the immediate environment.


  Thus at the root of all the confusion around production and reception of sound in alternative media like Helium, is that the vocal tract's non-linear characteristics are affected by the surrounding medium, whereas the ear's are not. That's it.

