1 / 12

Modifying the Helmholtz Resonance of Guitars and Drums

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

hawkinsc
Télécharger la présentation

Modifying the Helmholtz Resonance of Guitars and Drums

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related