Coupled oscillator models have been used for the low frequency response (50 to 250 Hz) of a guitar. These 2 and 3 mass models correctly predict measured resonance frequency relationships under various laboratory boundary conditions, but did not always represent the true state of a guitar in the players' hands. The model presented has improved these models in three ways, (1) a fourth oscillator includes the guitar body, (2) plate stiffnesses and other fundamental parameters were measured directly and effective areas and masses used to calculate the responses, including resonances and phases, directly, and (3) one of the three resultant resonances varies with neck and side mass and can also be modeled as a bar mode of the neck and body. The calculated and measured resonances and phases agree reasonably well.

Coupled oscillator models have been used for the low-frequency response (50–250 Hz) of a guitar [G. Caldersmith, “Guitar as a reflex enclosure,” J. Acoust. Soc. Am. 63, 1566–1575 (1978); O. Christensen, “Quantitative models for low-frequency guitar function,” in 103rd ASA Spring Meeting (1982) and J. Guitar Acoustics 6, 10–25 (1982); T. D. Rossing, J. Popp, and D. Polstein, “Acoustical response of guitars,” in Proceedings of Stockholm Music Acoustics Conference, Royal Swedish Academy of Music (1985), pp. 311–332]. These 2 and 3 mass models correctly predict measured resonance frequency relationships under various laboratory boundary conditions, but did not always represent the true state of a guitar in the players hands. The model presented has improved these models in three ways: (1) a fourth oscillator includes the guitar body; (2) plate stiffnesses and other fundamental parameters were measured directly and effective areas and masses were used to calculate the responses, including resonances and phases, directly; and (3) neck vibrations were calculated and measured and shown to effect the response significantly in some guitars. The calculated and measured resonances and phases agree reasonably well.

The mechanical responses of three freely supported guitars have been studied both under impulsive excitation and under excitation with a sinusoidal force [J. Popp and T. D. Rossing, J. Acoust. Soc. Am. Suppl. 1 76, S26 (1984)]. The normal modes of vibration as determined by the two different methods have been compared, and the agreement is found to be quite good. A comparison is made with the modes of vibration recorded in one of the guitars with the ribs fixed using time-average holographic interferometry.

The mechanical response of a guitar is characterized by a series of resonances and antiresonances which are related to the normal modes of vibration of the top plate, the back plate, and the enclosed air. The response depends on the manner in which the guitar is driven and especially the way in which it is supported. We compare the response of classical and folk guitars freely supported (with rubber bands) and with the ribs clamped as well as under other conditions. The resonances at low frequency compare favorably to the predictions of two-mass and three-mass models.

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