Wineglass Experiments
Jake
Purpose:
Originally to explore the similarities in the tones generated by rubbing the edge of the glass and by tapping it with a glass rod. Eventually we decided also to think about the overtones dampened or amplified by certain amounts of water.


Equipment:
We used one wineglass throughout the several days of testing, as well as a graduated cylinder calibrated in milliliters for measuring the water to be added after each set of trials. One short glass rod was used to tap the wineglass, though really any hard object would work. We used the LoggerPro software to record our results in Hz and Excel to organize them.



Procedure:
One person wet his fingers and then rubbed them on the edge of the wineglass until a stable tone was produced. The other held a microphone (connected to LoggerPro) approximately two inches from the edge of the glass, and then began recording. The recording was stopped once three visible and stable peaks were observed. Using the FFT Graph, the frequency of each of these peaks (the lowest and by far loudest dubbed “Tonic,” the next-lowest “Overtone 1,” and the next “Overtone 2”) was ascertained and entered into Excel under the relevant column (see Table 1). The process was then repeated, except instead of one person rubbing the glass, they tapped it with a glass rod instead. After three recordings each of rubbing and tapping, 20 mLs of water were added to the glass. (The experiment was started with 20 mLs rather than 0.)

At 80 mLs, a third overtone appeared quite close to the second. It was ignored on the grounds that we had nowhere to record it (simply adding a column in Excel would not have been useful) and that it was very small. However, it began growing and the second overtone began shrinking, until at 140 mLs the third was much larger than the second. We stopped the experiment there, as we did not know how to proceed and wished to think about the implications of such an appearance.



Data and Analysis: (all frequencies are measured in Hz)

mLs water
Tonic (Rubbing)
Overtone 1 (Rubbing)
Overtone 2 (Rubbing)
Tonic (Tapping)
Overtone (Tapping)
Overtone 2 (Tapping)
20
752
2256
3975
752
2080
3845
20
752
2256
3770
752
2060
3828
20
742
2265
3769
742
2070
3828
40
742
2265
3750
762
2070
3848
40
742
2246
3750
762
2070
3828
40
742
2246
3750
762
2070
3845
60
742
2246
3730
762
2070
3848
60
742
2246
3750
742
2070
3848
60
762
2246
3750
762
2070
3848
80
742
2246
3750
742
2070
3828
80
742
2246
3750
742
2070
3828
80
742
2246
3750
742
2050
3828
100
762
2227
3730
742
2052
3848
100
742
2227
3730
742
2070
3828
100
742
2246
3730
742
2051
3828
120
742
2227
3730
742
2051
3828
120
742
2227
3711
742
2051
3828
120
742
2227
3711
742
2070
3848


Table 1
Rub1/Tap1 (overtones)
Rub2/Tap2 (overtones)
1.085
1.034
1.095
0.985
1.094
0.985
1.094
0.975
1.085
0.980
1.085
0.975
1.085
0.969
1.085
0.975
1.085
0.975
1.085
0.980
1.085
0.980
1.096
0.980
1.085
0.969
1.076
0.974
1.095
0.974
1.086
0.974
1.086
0.969
1.076
0.964


Table 2
Overtone1/Tonic (rubbing)
Overtone 2/Tonic (rubbing)
3
5.286
3
5.013
3.053
5.080
3.053
5.054
3.027
5.054
3.027
5.054
3.027
5.027
3.027
5.054
2.948
4.921
3.027
5.054
3.027
5.054
3.027
5.054
2.923
4.895
3.001
5.027
3.027
5.027
3.001
5.027
3.001
5.001
3.001
5.001


Table 3
Overtone1/Tonic (tapping)
Overtone2/Tonic (tapping)
2.766
5.113
2.739
5.090
2.790
5.159
2.717
5.050
2.717
5.024
2.717
5.046
2.717
5.050
2.790
5.186
2.717
5.050
2.790
5.159
2.790
5.159
2.763
5.159
2.765
5.186
2.790
5.159
2.764
5.159
2.764
5.159
2.764
5.159
2.790
5.186


Table 4
Overtone2/Overtone1 (rubbing)
Overtone2/Overtone1 (tapping)
1.762
1.849
1.671
1.858
1.664
1.849
1.656
1.859
1.670
1.849
1.670
1.857
1.661
1.859
1.670
1.859
1.670
1.859
1.670
1.849
1.670
1.849
1.670
1.867
1.675
1.875
1.675
1.849
1.661
1.866
1.675
1.866
1.666
1.866
1.666
1.860
Table 5

Simply looking at the frequencies obtained (Table 1) gives rise to some interesting questions. It is clear that the tonic for rubbing did not change throughout the experiment: 742 appears over and over again, and although 752 and 762 are seen several times, it seems fairly clear due to their rarity and the fact that there is no pattern to their appearance that 742 is the true frequency here. The anomalies are also possibly due to misreading the FFT graphs: as the true peak is very narrow, it is easy to obtain the wrong frequency. That 742 is the true frequency is less clear when looking at the data for tapping: 762 is much more common near the beginning, with 742 only taking precedence near the end. However, since the microphones we used can only measure to an approximate exactitude of 20 Hz, this is dubiously significant. It was hypothesized that the frequency of the tonic only changes when the water passes a certain point on the glass, which point our 120 mLs did not touch.

The overtones, too, are fascinating. They are quite near each other in all cases—the first overtones for rubbing are almost always ~200 Hz higher than those for rubbing, the second overtones ~100 Hz higher.
In order to find a meaningful relationship between overtones and tonics, we tried to find ratios. First we divided the rubbing overtones by the tapping overtones and got relatively consistent ratios of 1.08 and .96 (Table 2). The numbers didn’t seem to have any particular significance, and nor did their inverses (not shown), so we moved on. We divided the first and second rubbing overtones by the tonic (Table 3), and found ratios of almost exactly 3 and 5. This seemed quite significant, and was in line with our expectations about how overtones arise: as even multiples of the frequency of the tonic. Unfortunately, when the same math was done with the tapping overtones (Table 4), it yielded nothing so exciting. The values were not as constant, and when averaged gave values of 2.75 and 5.12—moderately close to their rubbing counterparts, as expected since the overtones themselves were fairly close, but not particularly significant—and, it would seem, not actually overtones: they were not even multiples of the tonic.

I decided after the experiment was over to try and find a relationship between the overtones themselves (Table 5). Interestingly, the second rubbing overtone in all cases was almost exactly 5/3 the first one. The tapping overtones, however, did not give any such meaningful fractions—37/20.

The third overtone mentioned above was not recorded consistently. However, as an afterthought it was recorded once. It was found to be nearly exactly 11/5 the tonic (compared to the second overtone’s 10/5) but since it was only recorded once, this cannot be said to be reliable at all.
Since the experiment went in a different direction than intended, I will state both of the tentative conclusions that I have developed.

-Firstly, it seems that the creation of overtones is somehow interfered with when the glass is tapped rather than rubbed. It was suggested that the rod we used could be outputting harmonics itself, which would interfere with the frequencies the microphone detected. It was thought at the time that the material of the rod (glass) would be the cause, and so other materials were tested, all yielding the same frequencies. This could either mean that the material of the rod doesn’t matter, or that something else entirely is going on. I am inclined to believe the latter—perhaps the rod is in contact with the glass for too long, damping the waves.

-Secondly, it seems that filling the glass damps some overtones and amplifies others. This supports my conjecture that it is the glass that is vibrating, and that the water causes it to vibrate differently at different depths/volumes. The vast majority of the recorded numbers showed no change, and so after the experiment were treated as if they had been part of the same trial—i.e. as if the same amount of water had been present for all of them. Were I to do this experiment again, I would keep track of the amplitudes of the overtones as well, and leave room for new ones to come into play—it seemed obvious that, had we kept going, the initial second overtone would have disappeared entirely and the new third one taken its place.