Classical Guitar Design by Giuseppe Cuzzucoli & Mario Garrone

Author:Giuseppe Cuzzucoli & Mario Garrone
Language: eng
Format: epub
ISBN: 9783030329921
Publisher: Springer International Publishing

F2 = 213 Hz (basic resonance of the soundboard)

Fh = 129 Hz (Helmholtz resonance)

Fb0 = 215 Hz (natural resonance of the back in mode 〈0 0〉).

We get an estimated value for FB0 of 258.8 Hz, equal to the measured value (FB0 = 258 Hz).

The foregoing formula (of which we do not provide analytical proof) is congruent with the fundamental property of the coupled oscillators we have already run across: the sum of the squares of the resonant frequencies in the coupled system is equal to the sum of the squares of the resonant frequencies in the uncoupled system. In this particular case the soundboard (with its basic resonances), the Helmholtz resonator (with its resonance), and the back (with its natural frequency) come all into play.

The formula can be reversed to ascertain what the natural frequency Fb0 of the free back should be in order to get the target frequency FB0 for the closed back:

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