Plastic Coke Bottle Resonance

The cavity resonance frequencies of a 20 oz plastic coke bottle were recorded by blowing over the top of it and measuring the frequency using a microphone and a digital frequency counter.

Frequency dataCurve fitCalculation of frequency vs volume
Glass coke bottles of different size
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Plastic Coke Bottle Data

The cavity resonance frequencies of a 20 oz plastic coke bottle were recorded by blowing over the top of it and measuring the frequency using a microphone and a digital frequency counter.

Discussion of coke bottle resonanceCurve fit of data
Fill
(cm3)
Freq.
(Hz)
Air Vol.
(cm3)
0
178
646
25
182
621
50
184
596
75
188
571
100
192
546
125
197
521
150
202
496
175
209
471
200
214
446
225
221
421
250
229
396
275
236
371
300
244
346
325
256
321
350
268
296
375
287
271
400
294
246
425
318
221
450
340
196
475
364
171
500
406
146
525
445
121
550
496
96
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Curve fit of Plastic Coke Bottle Data

The cavity resonance data for a 20 oz plastic coke bottle was fit with a least squares line with the aid of the CricketGraph software.

Coke bottle resonance measurementsModeling of frequencies from curve fit
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Modeling Plastic Coke Bottle Resonance

You can calcutate the amount of water to add to sound a chosen frequency with a 20 oz plastic coke bottle. Use the curve fit to calculate the volume and subtract that from the total volume to predict the amount of water to add.

The curve fit of the resonance data leads to the expression:

If you want to sound frequency f = Hz, then the model gives a volume of cm3. This means that for a bottle of volume 646 cm3, you will have to add cm3 of water.

The practical range for this coke bottle is from about 180 to 500 Hz. This is about an octave plus a musical fifth near the middle of the piano, so most simple musical tunes can be produced with such bottles. From a musical score, you can find the associated frequencies from the equal tempered frequency list.

Cavity resonanceCoke bottle resonance Equal tempered frequency list
Frequencies for "Mary Had a Little Lamb"
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Mary Had a Little Lamb

The calculated frequencies for a 20 oz plastic coke bottle can be used to tune coke bottles to produce simple melodies. The tune for "Mary Had a Little Lamb" has only four notes. The coke bottle that was used had a measured total volume of 646 cm3.The frequencies and volumes for those notes are as follows.

Frequency (Hz)
Air volume (cm3)
Water volume to add(cm3)
196
524.5
121.5
220
428.7
217.3
246.9
349.5
296.5
293.7
256.0
390.0

Experimenters Michelle Miresse, Jeanne Urban and Kim Miller enjoy their production of "Mary Had a Little Lamb". Everyone else liked it too!

Coke bottle resonance measurementsModeling of frequencies from curve fit
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Resonance concepts
 
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