Preston P
Physics of Waves
Wineglass Work

Abstract
Hoping to expand upon the work done by Eva P, the 2009 Physics of Waves class, and Leah, we attempted to determine the relationship between volume of water, depth of water, and frequency of the note produced when a finger is rubbed around the top of a wineglass.

Equipment
Various wine glasses
Logger Pro
Vernier microphone (sampling rate of 10000 samples/second measuring frequencies in 20 Hz increments)
100 mL graduated cylinder, graduated in mL
50 mL graduated cylinder, graduated in mL
Meter stick, graduated in mm
Wood splints

Procedure
We added a predetermined amount of water, 50 mLs in trial 1 and 25 mLs in trial 2, to the wine glass. We then inserted a wood splint perpendicular to the surface of the water, reaching down to the deepest point of the glass. We removed the splint and, using the meter stick, measured the wet part of the split, which corresponded to the depth of the water.
While one person held the microphone, another then ran their finger around the rim of the glass. We watched the FFT graph of the sound until we determined which frequencies were consistently present and which were accidentally picked up by the microphone (such as shutting doors and voices). On certain trials we could identify overtones, but we ignored them and only recorded what we believed to be the tonic in any given trial.
Data was recorded in a notebook and then transferred to Microsoft Excel.

Data and Analysis
We recorded the volume of water, depth of water, and most prominent frequency per test in Table 1 and Table 2, corresponding respectively to Trial 1 and 2.

Table 1:
Volume (ml)
Depth (cm)
Frequency (Hz)
50
3.1
805.00
100
4.2
800.00
150
5.0
800.00
200
5.6
781.00
250
6.3
761.72
300
6.9
742.18
350
7.5
703.12
400
8.2
644.53
450
8.8
585.94
500
9.5
527.34
550
10.4
468.75
600
11.3
390.62

Table 2:
Volume (ml)
Depth (cm)
Frequency (Hz)
25
1.3
781.25
50
2.0
781.25
75
2.5
781.25
100
2.9
781.25
125
3.3
781.25
150
3.6
761.72
175
3.8
761.72
200
4.1
761.72
225
4.5
761.72
250
4.7
742.19
275
5.1
722.66
300
5.4
722.66
325
5.5
703.12
350
5.8
685.59
375
6.0
664.06
400
6.3
644.53
425
6.7
625.00
450
7.0
585.94
475
7.4
566.41
500
7.6
507.81
525
8.1
507.81
550
8.4
449.22
575
8.8
429.69
600
9.1
390.62

Volume and Frequency from Table 1 and Table 2 were graphed to create Figure 1 and Figure 2.

Figure 1:
Figure_2.png

Figure 2:
Figure_2.png

As can clearly be seen, our data is similar to that of the 2009 class and very different from that collected by Eva.

Depth and Frequency from Table 1 and Table 2 were graphed to create Figure 3 and Figure 4.


Figure 3:


Figure 4:


Because depth is directly proportional to volume, Figures 3 and 4 are not drastically different from Figures 1 and 2.

The correlation coefficient for Frequency to Depth in Trial 2 was only -0.9334, indicating that there is not a particularly strong relation between the two. However, the correlation coefficient for Frequency to Volume, a relationship we strongly believe exists, was only -.9402 in Trial 2. The correlation coefficients were -.9511 and -.9519 in Trial 1.

Correlation Coefficients for other possible relationships are recorded in Table 3.

Table 3:

Depth2 v. Frequency
Depth3 v. Frequency
Trial 1
-0.9864
-0.9933
Trial 2
-0.9843
-0.9941

Uncertainty Analysis
I think that part of the confusion in identifying the primary frequency of a given volume for a given wine glass is in distinguishing the tonic from its overtones. I would suggest that a group attempt this experiment not just looking for the tonic at a given water volume, but by completing a full harmonic analysis of every FFT graph. This would be time consuming, but would give very reliable data.

Ostensibly, the insensitivity of the microphone seems to present a challenge in mapping the change in frequency with volume. I believe that this was at least partially responsible for why we had the same frequencies for different volumes, especially when we were increasing volume in increments of 25 mls. While the change in frequency might be quantized, I think a given shift is far subtler than what the microphone is able to discern - As in, the frequency changes more rapidly than in jumps of 20 Hz. However, I am unsure if the microphone’s insensitivity actually obscured our data in any meaningful way.
A future experiment (for either math or physics) may be to find the depth of the water at 30-50 points and then construct a function that matches this data within the domain of the wineglass’s height. Using this function’s integral, a group may be able to find a relationship between depth and frequency.

Conclusion
Though our results were inconclusive, they support those reached by the 2009 Physics of Waves class.