# 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 data Curve fit Calculation 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 resonance Curve 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 measurements Modeling 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 resonance Coke 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 measurements Modeling of frequencies from curve fit
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