The Resonance of Common Bottles and Jugs

by

Donald R. Kanner

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Purpose

    Physics Teacher's Eyes Only: How would you like a lab for your students that does not involve an accepted conclusion that can be looked up in a physics text or on the internet?  

   Students:  How is resonant frequency related to the air found in a common bottle or jug?

Hypothesis

   P.T.'s Eyes Only:  Get your students to suggest a hypothesis that involves a known mathematical process, (examples: direct or inverse proportion), and a measurable air quantity, (examples: air height, air volume, air mass,  bottle neck measurements, etc.),  Be sure to warn your students that this hypothesis must not directly involve the amount of water that will be added to adjust the amount of air air in the bottle.

Recommended Library or Internet Research

    Check out the work of Hermann Ludwig von Helmholtz on the topic of resonance.

Materials Needed

   P.T. Supplies:  running water, graduated cylinders, rulers, a copy of the well tempered chromatic scale, and the items in the table below:

Low Tech, Low Cost

tuning forks, an octave or more from middle C on up.

   Here the student is limited to adding and removing water from the bottle to find the points where it resonates with each tuning fork.

Higher Tech, Moderate Cost

a set of musical instrument tuners, one for each lab group

   Get a tuner that will pinpoint any note on the chromatic scale.  The results for any quantity of air will be the note, such as C3, and the deviation from the note, plus or minus up to 50%.  Just look up the notes frequency and then adjust by adding the indicated percentage above or below to the next note on the scale.

Highest Tech, Big Bucks

desk top computers, condenser microphones and a site license for a  Real Time Analyzer program

   If your budget can afford it, this by far the best way.  Simply adjust the air in the bottle by adding or removing water, then blow across the bottle with the R.T.A. up and running.  The results will be a graph showing a spike and the frequency expressed to the nearest 0.1 Hz.

    Student  supplies:   his/her own bottle for analysis and perhaps his/her own TI-83.

Need I Say More?

    Each student must vary the air in his/her bottle, according to his/her hypothesis, by adding or subtracting water and collect the resonant frequencies which link to these bottle variations.  You know the rest, data and the results of calculations are tabulated, graphs are plotted, generalizations are made and future alternative experiments are discussed.  

 

    Physics Teacher's Eyes Only:  Should you  wish see an equation that will predict frequencies within a range of plus/minus two musical notes, e-mail me at drkanner@cps.edu



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