Hammered string (Piano string)

Model 850

33 × 7 × 26SchellenbergJ 47


Hammered string (Piano string)


This model depicts the solution of the one-dimensional oscillation equation: \[ \frac{\partial^2 y}{\partial t^2}= c^2 \cdot \frac{\partial^2 y}{\partial x^2}\ .\]

This equation describes for example the oscillation of a piano string or a guitar string. For this model as initial condition it was choosen a speedprofil in shape of a rectangular, with an additional rectangular in the center. This is called a hammer shape.

This kind of displacement happens at piano strings hit by a hammer. Additionally it is assumed that the string is fixed at the endpoints.

Identically constructed models were exhibited at a mathematical congress in Heidelberg in the year 1904 by the company Martin Schilling. Model 844 shows the same solution, the boundaries of the intervals are marked.

Text written by: Tim Bodenstein

Translated by: Lea Renner

Showcase of this model is Case number 49


Schilling, Martin(Hrg.): Catalog mathematischer Modelle, Leipzig(Verlag von Martin Schilling) 1911, 7.Auflage, No.362. p. 168.