Mark Rau –
Center for Computer Research in Music and Acoustics (CCRMA), Stanford University
660 Lomita Court
Stanford, California 94305, USA

Popular version of paper ‘1aMU2’ Measurements and Analysis of Acoustic Guitars During Various Stages of Their Construction
Presented Tuesday morning 9:50 – 10:05am, June 08, 2021
180th ASA Meeting, Acoustics in Focus

Stringed instruments have an internal structure which determines how they vibrate and produce sound when driven by the strings. This internal structure is made up of multiple vibrational resonances and is referred to as the resonant structure. Many stringed instrument builders (luthiers) will take acoustic measurements of instruments as they are being built to probe the resonant structure and make changes so that the instrument will sound as intended. However, the resonant structure of the instrument continuously evolves throughout the construction process, so it is unclear at which stage the acoustic measurements should be made.

To address this, we measured the resonant structure of three guitars during their construction. Two guitars are of the Orchestra Model (OM) style and were made by the Santa Cruz Guitar Company. The third is an 000-28 style guitar built by the author. The guitars were measured at multiple stages while being constructed, including: during the bracing of the top, construction of the box, sanding, application of polish, and once fully constructed. The stages of construction of the 000-28 are shown in Figure 2.

guitarsFigure 1: The three guitars in their completed state. The left and center guitars are the OMs and the right guitar is the 000-28.

Figure 2: Various stages of the 000-28 construction.

The resonant structure was measured by using a small hammer to impart a force to the instrument, and a laser Doppler vibrometer to measure the resulting vibrations. This provided the frequency and amplitude of each structural resonance as well as how long it would ring once struck.

Figure 3: Vibration measurement setup.

The lowest resonances are the most important, because they fall near the fundamental frequencies of most notes on the guitar, so we tracked how the first three prominent resonances changed. Figure 4 shows the frequency response of the 000-28 with the box constructed and sanded (top right of Fig. 2) and the guitar fully constructed (bottom right of Fig. 2). The lowest three prominent resonances are circled and their structural mode shapes are shown for the guitar box.

Figure 4: Frequency response of the 000-28 box (left) and completed guitar (right). The lowest three prominent resonances are highlighted.

We observed some general trends as the guitar evolves, such as the resonant frequencies and amplitudes decreasing as the guitar nears completion, particularly as the polish is applied. If one is trying to achieve a specific sonic quality from an instrument, we recommend taking measurements before the final sanding and adjusting the amount of sanding based on these observations. Final alterations can be made by carving the braces through the sound hole.

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