885095978

ments the impedance presented by thc bow to the string was deter-mined. The method for measuring string motion is based on earlier work [B. Ricca, G. Weinrdch, and N. R. Michad, J. Acoust. Soc. Am. Suppl. 1 86, S15 (1988)1. By it, the impedance presented by the bow to the string both parallel and perpendicular to the bow hair is determined. Some resulis will bc presented. [Work supported by NSF.]

3-30

3MU3. Violin admittance measurements using a one-dimensional mass-loading technique. Lcvon L. Yoder (Dept. of Physics, Adrian College, Adrian, MI 49221)

The input admittance of a violin can be determined from load/no-load measurements of the vibration velocity of the bridge [Weinreich and Yoder, J. Acoust. Soc. Am. Suppl. 1 81, S83 (1987)]. In the most successful of these expcriments [Boutillon, Weinreich, and Michael, J. Acoust. Soc. Am. Suppl. 1 84, S179 (1988)], the load was a mass attached directly to the bridge. Since the bridge motion is three dimen-sional, the load impedance is also. The problem involved a 3 X 3 admittance matrix and required ninc load/no-load measurements. This was accomplished by using three different acoustic irradiating fields and measuring the vibration velocitics in each of the three directions. This paper presents a method of applying a one-dimensional load to the bridge by attaching a cylindrical mass to one end of a long sewing needle and immersing it in an air column to form a surrounding air cushion and to hołd it upright. The data acquisition and analysis are reduced to three independent problems requiring only one acoustic field and sepa-rate mass loading for each direction. The admittance can be studied as a problem in one, two, or three dimensions. Experimental results in two dimensions will be presented.

ysis as well as by scanning with an accelerometer as the soundboard is driven by a smali shaker. Nodal lines tend to follow the stiff transverse ribs. Model shapes indicate that the transverse stiffness is substantially greater than the longitudinal stiffness in the braced soundboard. The impedance at most points on the bass bridges shows a maximum around 100 Hz and then falls off at roughly 6 dB/octave. The impedance on the treble bridges, on the other hand, reaches a broad maximum around 2 kHz and falls off quite slowly with frequency, at least up to 5 kHz.

4:15

3MU6. Numeri cal and physical experiments on hammer and piano strings. Antoine Chaigne (TELECOM Paris, 46 Rue Barrault, 75634 Paris Cedcx 13, France), Anders Askenfclt, and Erik V. Jansson (Dept. of Speech Commun. and Musie Acoust., Royal Inst. of Technol. (KTH), P.O. Box 700 14, S-100 44 Stockholm, Sweden)

Numerical experiments have been madę on the piano string with a discrete model using a finite difference calculation procedurę. The string model was previously applied to thc guitar [A. Chaigne, J. Acoust. Soc. Am. Suppl. 1 88, S188 (1990)] and is now tested with experimentally obtained data for the piano. The numerical experiments include system-atic variations of parameters such as hammer velocity and nonlinearity of the felt hammer and their influence on generated waveforms and spectra. Earlier physical experimcnts on pianos have provided dala on the velocity of the hammer and the string. In addition, the hammer-string interaction force has been estimated by measuring the compres-sion of the hammer felt during string contact. Rccorded string tones and measured waveforms will be presented and compared with typical cx-amples of those calculated.

3:45

3MU4. Vibrational modes of piano soundboards. Herve Brelay^a> and Thomas D. Rossing (Dept. of Physics, Northern Illinois Univ., DeKalb. IL60115)

The vibrational modes of the soundboards have been compared in two smali upright pianos: one of solid spruce and one of three layers (two thin layers of spruce with a core of poplar). The model frequencies are quite similar, although the modę shapes are somewhat different. In the spruce soundboard, the bending wave velocities for the low-frequency modes appear to increase with the square root of frequency, which suggests that the stiffness of the soundboard plus the ribs is approximately the same along and across the grain (i.e., the soundboard is fully compensated). In thc layered soundboard, on the other hand, the nodal lines tend to follow the ribs, indicating that the soundboard is overcompensated. Modę damping does not appear to bc substantially different in thc two soundboards.³ ^change student from Ecole Natio-nale Supericure des Telecommunications, Paris.

4:00

3MU5. Acoustics of a yangqin. Jianming Tsai and Thomas D. Rossing (Dept. of Physics, Northern Illinois Univ., DeKalb, IL 60115)

The yangqin is a Chinese hammered dulcimer with a tmpeanidal soundboard. It is played with two bamboo hammers and is used as a solo instrument as well as in Chinese traditional musie ensembles. The instrument we studied, approximately I m by 0.5 m, has 54 notes cov-ering a 4-octave rangę G₂ to G₆ (98-1568 Hz). It has five bridges and a total of 125 strings with sliders and rollers for fine tuning and for rapid modulation. The soundboard, which is crowned to a height of 4 cm in the center, is supported by seven unequally spaced transverse ribs. The ribs also divide the body into eight air chambers, which are connected by four or five holes (2.8 cm in diameter) through each rib; it is not elear whether these air chambers play an important role in the acoustics of the yangęin, however. Yibrational modes of the soundboard in the frequency rangę 100-700 Hz have been studied by impact modal anal4:30

3MU7. Numerical model i ng of guitar radiation fields using boundary elcments. Matthcw Brooke and Bernard E. Richardson (Dept. of Physics, UWCC, P.O. Box 913, CardifTCFl 3TH, Wales, U.K.)

Boundary element (BE) methods havc been used to supplement an existing numerical model of the classical guitar. This model computes, from fundamental parameters, the transfer between the plucking force at a point on the string and the acoustic pressure at the listening point. Structural modę shapes are determined from finite element (FE) analysis. The computcd surface velocities are then used to determine the coupling between the top piąte and strings and also the coupling between the top piąte and Helmholtz air resonance of the body cavity. The resultant acoustic radiation is calculated using the BE formulation, in which the entire surface of the guitar body is dividcd into boundary elements with surface velocities being specified over the top piąte and zero elsewhere (to simulate “rigid” back and sides). The computed radiation fields will be compared with measurements on real systems. Futurę work will involve coupling of the FE and BE methods in order to account for fluid loading.

4:45

3MU8. Time domain simulation of flute-like musical Instruments. B.

Fabre (Laboratotre d'Acoustique Univ. Paris VI, Tour 66, 4 PI. Jussieu 75005 Paris, France and Univ. du Maine, Le Mans, France) and A. van Steenbergen (Eindhoven Univ. of Technol., 5600 MB Eindhoven, The Netherlands)

The time-domain description of musical flute-like instruments as proposed by Mc Intyre, Schumacher, and Woodhouse [J. Acoust. Soc. Am. 74, 1325-1345 (1983)] has not yet been fully exploited. A major problem is thc very slow transient beharior of the model. For such modcls, based on the analysis of Fletcher [J. Acoust. Soc. Am. 60, 926-936 (1976)], the nonlinearity is only due to the jet drive saturalion. The transient behavior is linear because this nonlinearity is “smooth” and does not affect Iow amplitudę oscillations. Linear theory is most

1878

J. Acoust. Soc. Am.. Vol. 89, No. 4. Pt 2, April 1991

121 st Meetiog: Acoustical Society of America

1878