Piano acoustics - Wikipedia
Piano acoustics is the set of physical properties of the piano that affect its sound. It is an area of study within musical acoustics.
The strings of a piano vary in diameter, and therefore in mass per length, with lower strings thicker than upper. A typical range is from .240 inches (6.1 mm) for the lowest bass strings[1] to .031 inches (0.79 mm), string size 13, for the highest treble strings. 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 will vibrate with a pitch one octave lower than the shorter. However, if one were to use this principle to design a piano, i.e. if one began with the highest notes and then doubled the length of the strings again and again for each lower octave, it would be impossible to fit the bass strings onto a frame of any reasonable size. Furthermore, when strings vibrate, the width of the vibrations is related to the string length; in such a hypothetical ultra-long piano, the lowest strings would strike one another when played. 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 shorter than the "double with each octave" rule would predict, and are much thicker than the others.
The other factor that affects pitch, other than length, density and mass, is tension. Individual string tension in a concert grand piano may average 200 pounds (91 kg), and have a cumulative tension exceeding 20 tonnes (20,000 kg) each.
