In many films/television series/videogames, a character who has been reduced to minuscule size either by magic or advanced technology suddenly starts to speak with a very high-pitched, squeaky voice- has there ever been a reason stated for this?
In the real world smaller versions of things tend to make higher sounds than big things.
Think of :
- a double bass vs a violin
- a big drum vs a small drum
- a big drill vs a small drill
- the bong of a big bell vs the ting of a small bell.
The actual mechanical reasons why this happens may vary from object to object, but the common experience is that small things make higher sounds than large versions of the same thing.
It's really only logical to think that a person shrunk by magic or SF-handwavium would find their voice getting higher.
Providing the physics background to the other answers:
Sound is transmitted as a wave. The frequency of the sound generally corresponds to what we know as pitch. The frequency f is inversely related to the wave length λ via the speed of sound c, as in f = c/λ or λ = c/f. In other words, the higher the frequency (pitch) of a wave, the shorter your wave, or the longer the wave the lower your frequency.
Any noise is just swinging air molecules that reach your ear. Music instruments will vibrate (i.e. a swinging string or drumhead, a vibrating triangle, a "vibrating" air column in a flute). The lowest possible note will have the longest wave length and corresponds to the string length, air cavity etc.
As the other answers have pointed out, smaller people have smaller vocal chords, which are, grossly simplified, like a guitar or violin string. Thus they can not create as low notes as humans with regularly sized vocal chords.