Wine Glass Experiments
Jasper W-B
Sascha P
Jackson T
Kim T
Griffin G-B

Abstract
We ran a series of experiments to try to decipher how a wine glass produces a regular tone when a finger is rubbed around the rim, modeled after work done by Leah S. in 2008. We had a rough hypothesis that the walls of the glass were vibrating. We knew that the adding water to the glass would lower the pitch of the sound. We speculated that the water pushing on the walls of the glass might oppose the restoring force of the vibration and lead to a lower frequency.

Equipment
Glass 1 had a bowl that held approximately 600 mL with a depth of XXX and a rim diameter of XXX. (See Figure 1)
Glass 2 had a bowl that held approximately 600 mL with a depth of XXX and a rim diameter of XXX. (See Figure 2)
Glass 3 had a bowl that held approximately 550 mL with a depth of XXX and a rim diameter of XXX. (See Figure 3)
Veriner LabPro interface
Vernier microphone (sampling rate of 100 samples/second and measuring frequencies in 20 Hz increments)
cornstarch
100 mL and 25 mL plastic graduated cylinders, each graduated in 1 mL increments

Figure 1 Figure 2
Wine_Glasses_001.jpgWine_Glasses_003.jpg
Figure 3
Wine_Glasses_002.jpg
external image clip_image002.jpg external image clip_image004.jpg external image clip_image006.jpg

Procedure:
In the first set of experiment one researcher produced a sound with Glass 1 by running a moistened finger around the rim while another sampled the sound with the microphone. We monitored an FFT graph (Figure 4) of the sound and waited for a clearly defined peak valued. We stopped sampling at that point and recorded the peak value.
Figure 4
external image clip_image008.jpgFigure_4.jpg
We added 50.0 mL water to the glass and took another measurement. We repeated this process until the glass contained 600 mL, at which point the water level made it difficult to continue. The trials were run twice more for Glass 1. This data is recorded in Table 1.

Three trials were run under the same procedure with Glass 2 and recorded in Table 2.

One person ran a single set of trials with Glass 3, although the difficulties of doing this alone led to a broader margin of uncertainty.

We then tested the effects of adding a non-Newtonian fluid to the glass rather than water, adding a cornstarch/water mixture to Glass 1 in 50 mL increments (See Table 3).

We also tried added salt grains, 50 mL at a time to an empty glass. We did the same with fine quartz sand. We abandoned this line of research on discovering that we could not get a consistent sound after 100 mL of grains had been added.

Finally, we tested the effect of the density of the fluid added. A volume of 300.0 mL of water was added to Glass 2. A sample was collected by using the standard protocol. The water was poured off. We added 5.00 g NaCl and stirred to dissolve. We measured out 300.0 mL of the solution into Glass 2 and took another sample. This procedure was repeated, adding 5.00 g more of NaCl, for 18 more trials, ending with a solution of 90.00 g salt in300 mL of water. This data is recorded in Table 4.

Data and Analysis

Table 1 shows the frequencies from Glass 1. The repeated frequencies in a single trial are thought to occur because the microphone measures frequencies in increments of 20 Hz. Assuming that, for example, the frequencies actually did decrease over the addition of the first 150 mL in Trial 1, we chose to graph the frequency of 801 Hz as occurring when there were 75 mL (the midpoint of the range) of water in the glass. Making similar decisions for other occasions that there were repeated frequencies, we generated the first section of Table 5.


Table 1
Volume of Water
Frequency (Hz)
(mL)
Trail 1
Trial 2
Trial 3
0
801
820
801
50
801
801
801
100
801
801
801
150
801
801
801
200
762
781
762
250
762
762
762
300
742
742
742
350
684
703
684
400
645
645
645
450
586
586
586
500
527
527
527
550
449
449
469
600
391
410
410


Table 5
Volume of
Peak Frequency (Hz)
water (ml)
Trial 1
Trial 2
Trial 3
Trial 4
Trial 5
Trial 6

(Glass 1)
(Glass 2)
(Glass 3)
0
-
820
-
-
1074
-
25
-
-
-
1074
-
-
75
801
-
801
-
1055
762
100
-
801
-
1055
-
-
150
-
-
-
1035
1035
-
200
-
781
-
1016
996
742
225
762
-
762

-
-
250
-
762
-
957
957
703
275
-
-
-
918
918
-
300
742
742
742
898
898
684
325



859
859
-
350
684
703
684
820
820
645
375



762
762
-
400
645
645
645
723
723
605
425



664
684
-
450
586
586
586
645
645
547
475



586
586
-
500
527
527
527
547
-
508
550
449
449
469
-
-
430
600
391
410
410
-
-
-

Graph 1 shows the modified data from Trial 1. There is clearly a pattern, but is it not
Graph_1.jpg
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linear. We ran a regression analysis, testing for the cases listed in Table 6 along with their correlation coefficients. The values show that the best correlation in every case is for the square of volume of added water versus the peak frequency. That correlation coefficient in tat case is negative, indicating that frequency varies inversely with the square of volume of water in the glass.

Table 6: Correlation Coefficients





Glass 1
Glass 2
Glass 3

Trial 1
Trial 2
Trial 3


Volume vs Frequency
-0.9523
-0.9421
-0.9581
-0.9629
-0.9371
Volume vs Frequency^2
-0.9707
-0.9607
-0.9734
-0.9775

Volume^2 vs Frequency
-0.9961
-0.9959
-0.9969
-0.9979
-0.9940
Volume^3 vs Frequency
-0.9929
-0.9889
-0.9893
-0.9851

Volume vs ln(Frequency)



-0.9413

Volume vs log(Frequency)



-0.9413

Volume vs 1/log(Frequency)



0.9336

Volume vs 1/Frequency



0.9132









The next question we considered was the effect of the shape of the glass. Graph 2 shows the square of volume of water in the glass versus peak frequency. We see that the slope of the regression line differs for each glass. The slope is steepest for Trials 4 and 5, indicating the greatest change of frequent for a given volume of water. We note that this glass has the straightest sides and that the addition of a given volume of water produces the greatest change in the depth of the water. We would expect this to damp the motion of a greater portion of the walls of the glass and so it seems consistent with our hypothesis. This leads us to speculate that it would be valuable to graph pitch versus depth of water rather than volume of water.

Graph 2
external image clip_image012.gifGraph_2.jpg
Continuing the analysis in this vein, the most spherical glass (Glass 3) has the
shallowest slope. Glass 2 has a shape between that of the others, being taller and rounder that Glass 1 yet less spherical than Glass 3, and the slope of its graph is between that of the others.

We also note that the trend from Glass 1 to 3 to 2 parallels the lengths of the stems of the glasses. We suspect this is coincidence: we were able to hold the sounding glasses firmly by the stems without any evident effect on the sound, suggesting that the stem is not involved in the production of the sound.

On a related topic, we noted that we could produce a sound by running a moistened finger around the rim even when we held the ball of the glass, but only up to a point about a third of the way up from the bottom. That is about the same level the sand and salt were at when we could no longer produce a clear tone in the few trials we completed with those substances.

Our remaining trials explored the effects of varying density on the pitch. Table 7 shows results from our experiment with salt water in Glass 2. The frequency
Table 7
Mass of salt in
Peak Frequency
300 mL solution (g)
(hz)
0
898.44
5
898.44
15
898.44
30
878.91
45
878.91
60
859.38
75
859.38
90
859.38
decreased as the density increased. The fact that frequencies were sampled only ever 20 Hz set limits on how much more we can read in the data.

We also checked the frequency changes with changes in added volumes of a non-Newtonian fluid (Oobleck) to Glass 1. The results are in Table 3. Comparing these values with Table 1 it is seen that the peak
Table 3

Volume Oobleck (mL)
Peak Frequency (Hz)
75
801
200
762
250
723
300
703
350
664
395
605
frequency up to volumes of 200 mL are the same as those for water in Glass 1. After that, however, the frequencies are lower. This comparison is made visually in Graph 3. Graph 3 shows the water trials and the Oobleck trial done in Glass 1. The slope of the Oobleck line is very close to that of the lines of the water trials. It also starts (and ends) at a lower pitch. We speculate that this is due to the density of the cornstarch-saturated water being greater than that of plain water and thus offering greater resistance to the motion of the walls of the glass. This, then, is also consistent with our hypothesis.

Graph 3external image C:%5CDOCUME%7E1%5Cjheiles%5CLOCALS%7E1%5CTemp%5Cmsohtml1%5C01%5Cclip_image002.gif
Graph_3.jpg
The slope of each of the four lines was such that all had slopes within 4% of the central value of -1.3 x 10-3 Hz/mL3. The slopes are shown in Table 4

Table 3
Trial
slope (X 10-3 Hz/mL^2)
1
-1.21
2
-1.24
3
-1.15
Oobleck
-1.26