While it is fun to use helium to make your voice high and squeaky, it is actually equally fun to know why it does that. Something important to keep in mind about helium and voices is that helium does not change your voice, it changes the timbre of your voice - and yes there are plenty of studies to back that up. For the purposes of our discussion though, let’s just keep it simple and refer to the effect helium has on the sound of a voice as a voice change.
When you speak in your normal day to day life, air goes from your lungs, through the larynx, and then out of your mouth. On the way out, air passes under a pair of vocal folds making them vibrate. That vibration in turn gets the molecules in your vocal tract whipped up into an excited state which causes resonant frequencies which then escape the mouth with the air creating a sound. The sound is then manipulated by using your tongue, lips, soft palate, and various things like jaws clenches.
Every little change in the manner you allow air to escape your mouth when you are speaking changes the way it will sound. With that said, each individual has specific frequencies certain sounds are made at which are somewhat like a vocal fingerprint. With the basics of how speech is made, why does helium change all that?
Helium is lighter than air which means the speed of sound in helium is faster than in air. It is less dense so speed travels through it faster and easier. Your vocal tract does not change at all. It is a total myth that helium partially or temporarily tightens or paralyzes the vocal chords, or any number of weird things that float around as the answer. The second half of the answer is that even after inhaling helium, the wavelength of your voice remains constant. What helium does is increase the frequency of the sounds you make.
Look at it from another angle. We know speech is made up of several different elements. By inhaling helium, all of the elements except one change, and it is the change to the frequency which helium creates the high pitched squeaky voice. By the same token, if you were for some reason able to get your hands on xenon gas which is denser than air you would slow down the speed of sound and have a deeper voice.
After all of that is said and done, helium makes your voice sound high pitched and squeaky because it increases the speed of sound escaping your mouth. It has nothing to do with tightening vocal chords, your lungs expanding more, or some alien magic. It’s just a simple matter of acoustics that changes the timbre of your voice.