Answer
The density of helium is much lower than that of air.
Work Step by Step
The size of the throat, lungs, etc. determines the wavelengths of sound that a person produces. The associated frequencies are given by $f = \frac{v}{\lambda}$.
The speed of sound in helium is about 3 times the speed in air. After the person has inhaled helium, the produced sound frequencies rise by about a factor of 3, making the person sound high-pitched.
