Nia Hadi T, Jain Ankita D, Liu Yuming, Alam Mohammad-Reza, Barnas Roman, Makris Nicholas C
Department of Mechanical Engineering , Massachusetts Institute of Technology, 77 Massachusetts Avenue , Cambridge, MA 02139, USA.
Violin Making, North Bennet St. School , 39 North Bennet St. , Boston, MA 02113, USA.
Proc Math Phys Eng Sci. 2015 Mar 8;471(2175):20140905. doi: 10.1098/rspa.2014.0905.
The fact that acoustic radiation from a violin at air-cavity resonance is monopolar and can be determined by pure volume change is used to help explain related aspects of violin design evolution. By determining the acoustic conductance of arbitrarily shaped sound holes, it is found that air flow at the perimeter rather than the broader sound-hole area dominates acoustic conductance, and coupling between compressible air within the violin and its elastic structure lowers the Helmholtz resonance frequency from that found for a corresponding rigid instrument by roughly a semitone. As a result of the former, it is found that as sound-hole geometry of the violin's ancestors slowly evolved over centuries from simple circles to complex f-holes, the ratio of inefficient, acoustically inactive to total sound-hole area was decimated, roughly doubling air-resonance power efficiency. F-hole length then slowly increased by roughly 30% across two centuries in the renowned workshops of Amati, Stradivari and Guarneri, favouring instruments with higher air-resonance power, through a corresponding power increase of roughly 60%. By evolution-rate analysis, these changes are found to be consistent with mutations arising within the range of accidental replication fluctuations from craftsmanship limitations with subsequent selection favouring instruments with higher air-resonance power.
小提琴在气腔共振时的声辐射是单极的，且可由纯体积变化来确定，这一事实被用于帮助解释小提琴设计演变的相关方面。通过确定任意形状音孔的声导，发现音孔周边的气流而非较宽的音孔区域主导声导，并且小提琴内部可压缩空气与其弹性结构之间的耦合使亥姆霍兹共振频率比相应刚性乐器的共振频率降低了大约一个半音。基于前者的结果，发现随着小提琴祖先的音孔几何形状在几个世纪里从简单的圆形缓慢演变为复杂的f形音孔，低效、声学上不活跃的音孔面积与总音孔面积的比例大幅下降，空气共振功率效率大致提高了一倍。在阿马蒂、斯特拉迪瓦里和瓜奈里等著名工坊中，f形音孔的长度在两个世纪里缓慢增加了约30%，通过相应地提高约60%的功率，使具有更高空气共振功率的乐器更受青睐。通过进化速率分析，发现这些变化与因工艺限制导致的偶然复制波动范围内出现的突变一致，随后的选择有利于具有更高空气共振功率的乐器。
