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ES 240 project: Analysis of Resonance in Wine Glasses

We studied in class the phenomenon of resonance in forced, damped oscillators.  The mass and stiffness of a one-dimensional oscillator give rise to a natural frequency of oscillations known as the resonance frequency.  With no damping, energy input at this frequency accumulates and the amplitude of vibrations increases.

The phenomenon of resonance generalizes to linear elastic materials with many more (ie infinite) degrees of freedom: energy input at a natural frequency of vibration will accumulate and result in increasing amplitude of vibration.  The natural frequency in this case is determined by material properties (ie Young's modulus) and the geometry and dimensions of the object (ie a wine glass).  With so many degrees of freedom, the resonance frequency of common objects may be impossible to calculate exactly and it may be necessary to use the finite element method to investigate resonance.

In my project I propose to make some quick analytical estimates of the resonance frequency of a wine glass and compare them against numerical calculations from ABAQUS.  The accuracy of both of these methods may be assessed by a well known experiment.  Dip your finger in water and run it slowly around the rim of a wine glass.  A sound is emitted at the resonance frequency of the glass.  Whole instruments and music are devoted to this occurrence!  See the following website:

http://science.howstuffworks.com/question603.htm

Another interesting website with a movie showing a very practical result of resonance.

http://www.physics.ucla.edu/demoweb/demomanual/acoustics/effects_of_sound/breaking_glass_with_sound.html

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How dependent is the resonance frequency on the precise geometry of the wine glass?  

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