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Modifying the Helmholtz Resonance of Guitars and Drums

Investigating the impact of modifying the Helmholtz resonance on acoustic guitars and drums. Analyzing the O-Port device and creating a tunable cajon drum using simple harmonic motion principles. Exploring cavity volume variables and neck length extensions for optimizing resonance. Experimental measurements and frequency response tests conducted to enhance sound quality.

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Modifying the Helmholtz Resonance of Guitars and Drums

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  1. Modifying the Helmholtz Resonance of Guitars and Drums • Scott H. Hawley, Ph.D. • Chemistry & Physics Department • Belmont University

  2. Motivation • Better understand experimental results regarding “O-Port” device for modifying acoustic guitar sound. Manufacturer claims it makes guitar sound better; students found* it makes guitar sound worse. • Creation of a tunable cajon drum * “The O-Port: An Analysis” L. Gearhart, D. Jeffries, M. Rohr, N. Taylor PHY2010 Paper, Belmont U., Fall ‘09

  3. k m Amp. f f0 Simple Harmonic Motion • Consider a mass m on a spring with spring constant k: • When mass passes through equilibrium, it “overshoots,” resulting in oscillations. Oscillation frequency f0 has this proportionality: • Drive resonator at frequency f:

  4. Helmholtz Resonator t • A large cavity with a small opening & “neck” • HR is an acoustical simple harmonic oscillator • “Mass” is mass of air in neck, proportional to length t • “Spring constant” is inverse of cavity volume V (because air resists being compressed and “stretched”) • For neck area A & radius R, and sound speed v, V

  5. Parameters of the Model • Neck has total length t=to+ti, where to is above cavity and ti extends inside cavity A When ti=0, resonant frequency f0 has this proportionality: to ti V

  6. Extend Neck Into Cavity • Length above cavity is to. Then add length ti which extends into cavity: • Thus some of the volume of the cavity is converted into “neck volume”: • The new frequency f0’ has proportionality

  7. f0’/f0 ti Simplest Case: to+ti = const • Consider extending a pipe of constant length to+ti into the cavity to various depths ti. V=12x12x18, A=pR2, R={2,4,6}2 (Typical for cajon, if in inches) A sound hole radius of 2” is typical for cajons. Thus this method should be ineffective for creating a tunable cajon. R=6 t=2.0 R=4 R=2 t=0.5 t=0.1

  8. f0’/f0 to=2.0 to=1.0 to=0.5 to=0.1 ti Variable Neck Length • to={0.2,0.5,1.0,2.0}, V=12x18x{3,5,12}, A=pR2, R={1,2,3} • Cavity volume is not as significant a factor as “thickness of the top” near sound hole. cf. results of O-Port study.

  9. Cajon Measurements Thanks to Matthew “The Percussionator” Burgess for the Cajon! • Measured dimensions of cajon, calculated f0 = 82Hz via HR eq. • Ran sine wave sweeps with mic near & in cajon

  10. Cajon Freq. Response Tests performed via Room EQ Wizard(sine wave sweep) Rayleigh eq. tells us lowest “room mode” of box is (0,0,1) at 405 Hz.

  11. References • Kicak, P.,“Frequency and Dynamics Analysis of Bass Tone of Cajon Box Drum,” Proceedings of ACOUSTICS High Tatras 2009, 34th Int’l Acoustical Conference, 2009. • Remo, Inc., “Pitch Modulator Drum,” European Patent Application EP1909260A2, 2008.

  12. That’s all for now! • Further work: • Effects of varying the area A of the opening • Effects of lengthening to alone • Ways of varying the volume V • Comparison to dumbek drum

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