# Hammered string (Piano string)

### Model 850

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Size: | Constructor: | Category: |

33 × 7 × 26 | Schellenberg | J 47 |

### Description

Hammered string (Piano string)

### Additions

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.

Showcase of this model is Case number 49

### References

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