# Why does a wine glass with less water resonate at a higher frequency?

In this video https://www.youtube.com/watch?v=hWwM7F-zaHs, Professor Lewin showed that for the tube, the less water there is, the longer the effective length of the tube and therefore, the lower the frequency.

He then demonstrates an opposite effect for a wine glass. Namely, an empty wine glass resonates at a higher frequency than a filled one. Why is that so?

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The qualitative reason is in the case of the pipe, the walls can be assumed for practical purposes to be rigid (i.e. they don't vibrate), and the resonant frequency of the vibrations in the air inside is determined by the boundary conditions. In other words, the shorter the air column in the pipe (more water), the shorter the wavelengths of the acoustic modes, or the higher the frequency. Or less water, lower frequency.

Whereas for the wineglass, the walls of the glass are thin enough that they cannot be assumed rigid - indeed they vibrate, and it is the vibrations of the glass that determine its resonant frequency.

With no water in the wineglass, the walls are not mass loaded beyond the mass loading due to the air inside. But as you add water, the mass of the water mass loads the vibration of the walls. Just as with a simple harmonic oscillator, the larger the mass, the lower the frequency of oscillation.

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For the pipe, it is the air that is vibrating. When the column of air is shorter the frequency is higher.

In the case of the wine glass, the glass (not the air) is vibrating. Add water and you increase the inertia of the glass, which lowers the frequency of the resonance. The air may also resonate - but for something the size of a wine glass the frequency is very high - inaudible compared to the vibration of the glass.

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In the case of the wine glass, why is the air resonance frequency high? Isn't it true that the more air, the lower the frequency just like the case of the pipe? – user52874 Jul 17 '14 at 11:45
The length if the column of air determines the frequency. Wine glass = short column. Plus the ratio of length to aperture is not favorable so most of the air doesn't "notice" it reaches the end of the pipe - this makes the wine glass a very poor resonator for air. Wrong shape, wrong size. – Floris Jul 17 '14 at 11:58