The Relationship Between Resonant Frequency, Sound Hole Diameter, and Body Depth in Acoustic Guitars

Alyssa Fernandez, Purdue University

Abstract

When a design feature (such as material choice, internal bracing pattern, guitar body depth, and sound hole diameter) of an acoustic guitar changes, the effect of the change on the guitar’s sound is not well understood. As a result, luthiers approximate how to make guitars that have resonant frequencies of around 95-105 Hertz (Hz), the frequency range which sounds “good.” The researcher designed a reconfigurable fixture that simulated an acoustic guitar body with a variable body depth and sound hole diameter. The researcher used this testing fixture to examine the relationship between sound hole diameter, body depth, and resonant frequency. She conducted an experimental parameter sweep, measuring frequency response functions (FRFs) to collect data on the first, Helmholtz, and second resonant frequencies of the simulated acoustic guitar. The researcher pinpointed the general trends in the correlation between resonant frequency, body depth, and sound hole diameter using the frequency data from the FRF measurements. She determined that as sound hole diameter increased, the first, Helmholtz, and second resonant frequencies increased; and as body depth and body volume increased, the first and Helmholtz resonant frequencies decreased, while the second resonant frequency increased up until a body depth of approximately 4.50” inches. Exploring alternative design features and material choices contributes to improving urban infrastructure by encouraging luthiers to make instruments with sustainable materials (National Academy of Engineering, Grand Challenges – Restore and Improve Urban Infrastructure, 2023).

Degree

M.S.

Advisors

French, Purdue University.

Subject Area

Acoustics|Music

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