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We all know that a wineglass can be made to vibrate and "sing" by rubbing our fingers...

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We all know that a wineglass can be made to vibrate and "sing" by rubbing our fingers against the rim of the glass. When using a liquid, I noticed that it would stop "singing" when it reached a certain volume in the glass. Why is this so? Also, is a wineglass classified as a vibrating membrane, or an air column?

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The most likely explanation for why the wineglass stopped singing, was not that it stopped singing, but that it reached a frequency you couldn't hear. 

If you've ever played around with this, you would observe that less liquid in the glass results in a lower pitch sound, and more liquid brings a higher pitch sound.  Different pitches are generated by different frequencies of sound waves.  But just as we can only see certain frequencies of light waves (less than 1/88th of the spectrum) we can only hear certain frequencies of sound.  There are sounds that are too high, or too low for us to hear.  That most likely happened with your wineglass.  The liquid level drove the pitch over the highest audible frequency. 

As for how to classify the wineglass.  The sound is generated by friction between the glass and your finger.  The water/wine on your finger reduces the friction but it is still there making your finger bounce along the rim making the glass itself vibrate, so it would be considered a vibrating membrane. 

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