Chladni mønstre: Chladni patterns

Johannes Holm, Princiya Annarajalingam & Sidsel D. Langpap

Studenteropgave: Semesterprojekt

Abstrakt

The project is based on an old experiment concerning vibrations in plates, the experiment allows for the visualization of the nodal lines associated with standing waves. The nodal lines form beautiful patterns, referred to as Nodal-patterns or Chladni-patterns after the German pioneer. The patterns can be divided into three groups; the perfect ones, the imperfect ones and the combined ones. The main purpose of this paper is to determine whether it is possible to develop a mathematical model based on the wave equation, capable of determining the specific blend ratio in a combined pattern produced experimentally. We develop a model that approximately represents the nodal patterns in our experiment. The patterns from our model are then visualized using the math program Mathematica. The model is based on the wave equation in two dimensions, which governs wave propagation in membranes, not in plates. Another purpose with our experiment is therefore to determine whether it is reasonable to hypothesize that a thin plate can be perceived as a membrane. The experiment was conducted with aluminium plates fastened to a mechanical vibrator with a screw in the centre. The vibrator was driven by a function generator, which allowed for the vibration frequency to be controlled with great accuracy. It is concluded from our analysis, that our model does not provide a very accurate representation of the experimental conditions, and therefore cannot determine the blending ratios with very great accuracy. The reason for this divergence is concluded not to be because of the hypothesis that we can consider a thin plate a membrane. But rather on the experimental conditions, with the plate being vibrated from its centre, which we have not been able to correctly incorporate into the model.

UddannelserBasis - Naturvidenskabelig Bacheloruddannelse, (Bachelor uddannelse) Basis
SprogDansk
Udgivelsesdato18 jun. 2007
VejledereAnders J. Hede Madsen

Emneord

  • vibrating plates
  • waves
  • wave equation
  • Chladni