What's in Your Wineglasss

You probably have done the trick of rubbing the rim of a wineglass, partially filled with water, to produce a crisp tone. We took this old instrument and applied a new question: What would happen to the frequency if we used liquids with different densities? A.P. French constructed a wineglass model which predicts that $(f_0/f)^2 = 1 + kF^4$, where $f_0$ is the frequency of the empty wineglass, $F$ is the wineglass fullness fraction, $f$ is the frequency at that fullness fraction, and $k$ is a constant that is proportional to the density of the liquid [1]. We addressed this question experimentally using five liquids with densities varying from $0.7-1.4\,{\rm g/cm^3}$. To determine how the frequency changed, we filled a wineglass to several different heights for each liquid. At each height, we made a digital recording of the sound produced and used FFT analysis software to determine its frequency. Our results show that the denser a liquid is the lower the frequency of the sound the wineglass produces. The results also confirm that A.P. French's model correctly predicts the relationship between frequency and density.\\[4pt] [1] A.P. French, \textit{In Vino Veritas: A Study of Wineglass Acoustics}, Am. J. Phys. 51, 8 (1983).