The Acoustics of Mandolins by Dave Cohen and Thomas D. Rossing
Abstract: Using electronic TV holography, we have studied the vibrational modes of four mandolins and a mandola. The lowest (0,0) modes may appear as a triplet (as in a guitar) or as a doublet. The modal frequencies correlate well with the frequency response curves. Sound spectra indicate that sound radiation is quite uniform over the 0-5 kHz range with some rolloff above 2.5 kHz.
from Acoustical Science and Technology, 24, 1 (2003), pp 1-6.

Normal Modes of Vibration in Two Mandolins by Dave Cohen and Thomas D. Rossing
Abstract: Using electronic TV holography, we have studied the vibrational modes of two mandolins of the Gibson F-type, one with f-holes and the other with an oval sound hole. Although the observed normal modes are moderately similar to those observed in guitars, the coupling between plate modes and air cavity modes appears to be weaker. Plate coupling is greater in the oval hole instrument, and we observe three (0,0) modes as in a guitar. In the f-hole instrument, a doublet (0,0) is observed.
from Catgut Acoustical SocietyJournal, Vol. 4, No. 2 (Series III), November 2000, pp 48-54.

Additional research on acoustical properties of pre-1929 mandolins presented in May 2004 to the Acoustical Society of America will be available in the near future.

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