I believe it all comes down to how the sound waves from your voice box interact with the gas. Sound waves move faster through the helium because it is lighter than the elements in regular air. This means the sound travels at a higher frequency so the sound becomes more high pitched.
Same principle with the sulphur hexafluride David mentioned, it is heavier than air so sound moves slower.
Make sure you don’t breathe in to much though because it can displace the oxygen in your lungs which is not a good thing.
It affects your voice, because your vocal cords vibrate differently in its presence and so produce waves that have a different wavelength .
You should be careful about inhaling it though, remember that if you breath pure helium there will not be any oxygen so besides a Mickey voice you can feel dizziness, headache and suffocation.
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