The frequencies of standing waves on an ideal string are spaced harmonically. That is, each higher mode of the standing wave is a multiple of the fundamental mode frequency. This is a fairly good model for thin, flexible strings, but breaks down for heavier, stiffer strings, such as the bass strings in a piano. Here the stiffness of the strings changes the wave equation and introduces dispersion. The result is that higher modes are “stretched” in frequency. For example, if the fundamental mode is 110Hz, the next mode will not be 220Hz, it will be a little higher. If this is the case, then there is no such thing as “proper” tuning of a piano, since it is impossible to have all the notes harmonically related. This leads to something called "inharmonicity".
The aim of this project is to first characterise the inharmonicity of piano strings and compare different designs of string. To do this we will use a rig that can tension some samples of piano wire and piano bass strings, then measure the acoustic properties of the string. The string samples come from the only maker of piano strings in Australia. They are interested to know if there is any difference between designs and whether it might be possible to engineer strings to control the degree of inharmonicity.
There is some information about pianos and the effect of inharmonicity here: http://asa.scitation.org/doi/abs/10.1121/1.416017