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Violin Design
March 23, 2015
There's an
Internet meme in which
site commentators offer to play a
sad song on the world's smallest
violin in response to some previous comment. If you type "world's smallest" into
Google search, the first
auto-complete choice is "world's smallest violin." This concept was used
as early as 2002 in the episode, "
Squilliam Returns (season 3, episode 8b)," of the cartoon series,
SpongeBob SquarePants.
In that episode,
Mr. Krabs (my favorite character in SpongeBob SquarePants) plays the world's smallest violin as
background music to several sad
monologues.[1] An unusual feature of the small violin is that its
notes are in the
tonal range of a regular violin, and they're just as loud. Unless the
strings are made from some exotic
material, these smaller strings couldn't produce the same
frequencies as violins of the standard size.
The
fundamental resonance frequency f of a string depends on the
length of the string
L, its
linear density ρ (which is the string
mass m per unit length), and the applied
tension T. All these variables should be familiar to even those who have played with toy
guitars, since the thicker strings give the lower frequencies, and tightening any string leads to a higher frequency.
So, a violin a tenth the size of a standard violin, presumably with strings a tenth the
diameter (giving a linear density one hundredths that of a normal string), would sound notes at a hundred times the frequency for the same tension. Since the
vibrational amplitude is likewise reduced, the notes would be much softer.
A violin fabricated by Jakob Stainer in 1658.
Stainer's instruments were popular in chamber music settings, but the Antonio Stradivari instruments were louder and preferred in orchestral settings.
(Via Wikimedia Commons.)
I wrote about the
evolution of the shape of the violin in an
earlier article (Violin Evolution, October 31, 2014). One feature that you'll notice from the above example are the "f" holes in the body of the violin. This shape is not just decorative, as a recent
paper in the
Proceedings of the Royal Society A shows. Earlier string instruments, such as the
lute, had simple,
circular holes. The "f" holes produce a louder sound.[2-3]
Mechanical engineers from
MIT teamed with a
Boston violin maker for this study in which an
analysis was done on hundreds of violins built in the tradition of
Cremona masters.[3] They isolated the design features that contribute to the acoustic power and fullness of sound of these violins.[3]
Acoustically, the sound production mechanism of a violin is simple. The vibrations of the strings are coupled by the
bridge element into the body, which acts as a sounding board, and also as a
Helmholtz resonator. All the sound
energy is derived from the vibration of the strings, but the placement of the bridge and the construction of the body determines how
efficiently this energy is transformed to useful
sound waves.
Stradivarius violins appear to have special sound quality, and there have been many
scientific studies to determine why this should be. Although their sound quality has been attributed to the
mechanical properties of the
wood used in their construction, or the
varnish and other
chemical treatments, the major determinant of violin sound is its
design.
This study came about by a question posed by a lute player to
Nicholas Makris,
coauthor of the study and a
professor of
mechanical engineering at MIT. The question was whether the
carvings within a lute's sound hole change the sound quality. In
collaboration with
fluid mechanics expert,
Yuming Liu, an MIT research scientist, he found that air flow was fastest at a hole's periphery, while its interior, whether open or partially blocked by
lacework, was not a significant factor affecting the air flow. [3]
In their studies, the researchers acquired
technical drawings of
historical violins of the 10th through 18th century from various sources, as well as images of the instruments made using
X-ray and
CAT scanners. They
correlated the instrument dimensions with the acoustical properties.[3] The
acoustic conductance of the sound holes, that is, the flow of sound waves from one side to the other, was dominated by the air flow at the
perimeter of the hole. As a consequence, violins with more elongated holes produce more sound.[3] These elongated holes also take up less
area, another factor that increases sound intensity by allowing more sounding board area. Other factors, such as having a thicker back plate, influence sound intensity.[3]
Evolution of stringed instrument holes from the 10th to 18th centuries. (MIT image, reformatted.)
The question arises as to whether the change in hole shape and the thickening of the back plate were done intentionally. The authors believe that the changes evolved by natural
mutation; that is,
craftsman error. These "errors" propagated to subsequent designs since they improved the sound.[2-3] Says Makris,
"You're cutting with a knife into thin wood and you can't get it perfectly, and the error we report is about 2 percent … always within what would have happened if it was an evolutionary change, accidentally from random fluctuations... Whether they understood, ‘Oh, we need to make [the sound hole] more slender,’ we can't say. But they definitely knew what was a better instrument to replicate."[3]
This research was funded in part by the
U.S. Office of Naval Research.[3]
Modeled air flow velocity shows that maximum velocity occurs at the perimeter of the holes. (MIT figure, reformatted.)
References:
- My maternal grandmother had a recipe for Krabby Patties long before the cartoon show. She would mix the contents of a can of tuna (oil-packed) with an egg, bread crumbs and optional seasoning, shape the mixture into a patty, and fry. My children used to enjoy these, but I would make them with water-packed tuna, drained, with added olive oil. There are various other recipes for Krabby Patties on the Internet, some of which sound better than this.
- Hadi T. Nia, Ankita D. Jain, Yuming Liu, Mohammad-Reza Alam, Roman Barnas, and Nicholas C. Makris, "The evolution of air resonance power efficiency in the violin and its ancestors," Proceedings of the Royal Society A, vol. 471, no. 2175 (March, 2015), DOI: 10.1098/rspa.2014.0905. This is an open access article with a PDF file available, here.
- Jennifer Chu, "Power efficiency in the violin," MIT Press Release, February 10, 2015.
Permanent Link to this article
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