David Cohen, dcohen7@juno.com
J. Sargeant Reynolds Community College
Richmond, VA 23261
Thomas D. Rossing
Physics Department
Norhtern Illinois University
DeKalb, IL 60115
Popular Version of Paper
4pMU2
Friday Afternoon, June 2, 2000
139th ASA Meeting, Atlanta, GA
The mandolin is a plucked string instrument whose origins appear to go back to the medieval gittern. By the beginning of the 20th centruy, the mandolin had developed into a concert instrument in Italy and other countries in Europe. In addition to virtuosi soloists, mandolin orchestras became popular. Mascagni, Leoncavallo, Puccini, and other opera composeers incorporated mandolins into their operas.
The mandolin was brought to America by Italian immigrants around the turn of the century. American instrument makers, such as Lyon and Healy and C.F. Martin produced thousands of mandolins, many of which were played in the popular mandolin orchestras. Inventor Orville Gibson designed two main types of mandolins, the A-type with a symmetrical body and the F-type with a scroll on the bass side that increased the size of the resonating chamber. In 1922, Gibson employee Lloyd Loar designed a mandolin with f-holes (like those of a violin) replacing the traditional sound hole.
Using holographic interferometry, we have compared the vibrational modes of two Gibson F-type mandolins, one with an elliptical sound hole and one with f-holes. The lowest mode of the body in both instruments is similar to that found in guitars. The top plate and the back plate move in opposite directions and the instrument "breathes" through the sound holes. This mode, which is observed at 318 Hzm in the f-hole mandolin, is observed at 423 Hz in the mandolin with the oval sound hole, which has a stiffer top plate. A second mode occurs at 377 Hz in the f-hole mandolin and at 480 Hz in the mandolin with the oval sound hole.
A pair of modes in which the plates rock side-to-side around a central nodal line occur at 524 and 546 Hz in the f-hole mandolin and at 579 and 644 Hz in the mandolin with the oval sound hole. Views of the top and back vibrating in this mode in the mandolin with the oval sound hole are shown left below. A higher mode at 1117 Hz in the f-hole mandolin, in which the plates vibrate in 4 segments, is shown right below.
The closer spacing of the vibrational modes in a mandolin, compared to a guitar, result in a smooth sound spectrum with fewer prominent resonances than are observed in a guitar. The weaker bass response of the mandolin with the oval sound hole appears to be due to a greater mismatch in frequency between the main (Helmholtz) air resonance of the body and the lowest modes of vibration of the top and back plates. A firmer bass response, if desired, would result from lowering the plate mode frequencies, by thinning the plates, and/or raising the Helmholtz air resonance by enlarging the sound hole.