String Length and Mass
The strings of a piano vary in thickness, and therefore in mass per length, with bass strings thicker than treble. A typical range is from 1/30 inch (.85 mm) for the highest treble strings to 1/3 inch (8.5 mm) for the lowest bass. These differences in string thickness follow from well-understood acoustic properties of strings.
Given two strings, equally taut and heavy, one twice as long as the other, the longer would vibrate with a pitch one octave lower than the shorter. However, if one were to use this principle to design a piano it would be impossible to fit the bass strings onto a frame of any reasonable size. Furthermore, in such a hypothetical, gigantic piano, the lowest strings would travel so far in vibrating that they would strike one another. Instead, piano makers take advantage of the fact that a heavy string vibrates more slowly than a light string of identical length and tension; thus, the bass strings on the piano are much thicker than the others.
Read more about this topic: Piano Acoustics
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