When Lily Wang's machine plays the violin suspended inside of it, the sound is hardly akin to Isaac Stern playing at Carnegie Hall. "It sounds less like music," Wang explains, "and more like noise."
The machine is not housed in anything like a concert hall either; instead it sits in a small room in Penn State's Applied Research Laboratory, surrounded by fiberglass wedges that look like giant hunks of cheese. Its skeleton is a five-foot tall square frame of black iron bars. At its heart is a specially designed structure on which the violin rests. A mechanical bowing arm swings down from the top of the frame. Wang handsews 30 horsehairs onto a belt to make the bow. "This belt has lasted for three series of tests," she says. "But I'm going to have to sew a new one soon. The hairs break." Wang finds a broken hair and clips it, weaving the loose end back into the other hairs.
Then she rubs a yellowish waxy rosin over the belt. "The rosin increases the sticking friction between the belt and the strings on the instrument. Violinists rub it on their bows all the time." She pulls a violin out of its small battered case, places it in the machine, checks its position, and then crosses the room to switch on the motor that powers the bowing arm. "I can control how fast the belt moves by adjusting the voltage." She twists a knob on the motor and the horsehairs turn like a small conveyor belt. Wang moves the arm so that it is millimeters away from the A string, like a violinist poised before the conductor. The belt touches down and the violin releases a loud and unwavering note. "You can hear the differences in sound when you stand in front of it," Wang walks around the cage, "on the side of it," she moves again, "and behind it." Wang touches the body of the violin. "You can feel it vibrating." She tilts the bowing arm so that it plays the D string; the violin produces a lower, deeper sound. Two minutes pass. Five minutes. The note drags on like an emergency signal on the radio. "Imagine listening to that for an hour," she says, raising her voice. "I have to wear earplugs." Wang pulls the arm away from the violin and the sound stops.
"It s harmonics that make music beautiful," Wang explains as she switches off the motor. "If I hum" hmmmm "I excite a large number of frequencies." Each frequency is a sine wave, a mathematical curve that looks like a series of crests and troughs. All of the sine waves added together produce the complicated sound that we hear. While a single sine wave looks like the smooth curves of a hill, the added sine waves resemble the jagged lines of a mountain range. "The interesting thing about many musical instruments is that the frequencies are all harmonically related Å the higher frequencies that the violin excite are all integer multiples of the lowest frequency," she explains. "Harmonics make the violin sound musical instead of noisy." Wang removes the violin from her machine and places it back in its case. "I rented this from a local music company." She laughs. "They think I m taking violin lessons."
Wang is a pianist, not a violinist; she began playing at age four. As an undergraduate, she studied both civil engineering and architecture at Princeton, spending her summers doing acoustics research at Georgia Tech and working with a consulting group in Connecticut. Wang is now a doctoral candidate in acoustics at Penn State. Since she was a young musician, she has dreamed of designing concert halls. "I've always wanted to bring art and science together in my life," she says.
Many of the students in the acoustics program share Wang's interests. "We could probably form an orchestra from the students in the department, although it might be a little heavy on the brass," says Courtney Burroughs, associate professor of acoustics and Wang's research adviser. "If we had the money for it, I imagine there would be a big long line to study the acoustics of musical instruments." He adds, "but there is very little funding for that kind of thing in this country." Burroughs admits that he talked Wang into the violin project. "She has a grant from the National Science Foundation and she could have done whatever she wanted," he says.
Although he is not a musician himself, Burroughs teaches a highly mathematical course on the acoustics of musical instruments. "Usually we apply what we know to plates and bars," says Wang. "He forces us to take the principles of acoustics and apply it to something real."
Wang and Burroughs conceived of their version of a violin-playing machine in 1995, soon after Wang s first year at Penn State. "Courtney and I sat down with all the requirements and said, 'How are we going to do all of this?'" Wang says. "I wanted to excite the violin with something like a bow, instead of a hammer or a mechanical shaker as some other people have done." The staff at the ARL machine shop helped Wang make some of the parts, including the complicated bowing arm. "They spent a lot of time helping me. I think they thought the project was really neat." Wang laughs. "They even painted part of it blue and white for Penn State." Hand-sewing horse hairs together to make the bow is Wang's job. "It's the most tedious part of my research, it takes forever," she says. "But the horsehairs are responsible for this very unusual stick-slip interaction that occurs when a person bows a violin."
Wang presented her research, "Characterizing the radiated sound field around a violin using near-field acoustic holography," to the general public at the 1997 Graduate Research Exhibition. "When most people think of holography," Wang says, "they think of the picture on their credit card." That kind of hologram is optical. It works like this: The pattern of light waves that reflect off an object is recorded onto a photographic plate. At the same time, a single light wave called a reference beam is captured, to form what is called an interference pattern. The interference pattern stores information about the light's magnitude and the phase, the degree to which the wave fronts are in sync with each other. "When you angle another light just right onto the hologram, the original image is reconstructed from the information stored in the interference pattern," Wang says, "and it appears three dimensional." Twist a MasterCard under lamplight and a globe appears; on the Visa it's a white dove.
Wang is using acoustical holography to reconstruct the sound field saround a violin. "Instead of capturing light waves on a photographic plate, we're recording sound waves via microphones," she says. Wang uses a computer program to turn sound wave measurements made around her violin into a colorful energy map. "We can then determine what part of the body the sound waves are coming from," says Burroughs.
Next to Wang s violin-playing machine stands a vertical array of 15 microphones, each held in a small piece of PVC pipe. The pipes are attached to an arm that moves them left and right, up and down. Wang takes measurements at points very close to the violin on four planes that make a box around it: the front, the back, and the sides. "It takes about an hour and a half to make measurements on each side," she explains.
As the violin plays, the microphones record the sound, or pressure waves that travel through the air. The pressure measurements, including the magnitude and phase of the waves, are fed into a computer program that reconstructs the sound field on any plane parallel to the measured plane. Another computer program makes the colorful representations of the mathematical data.
The whole idea is to see how a violin radiates," says Wang. Detachable blocks on the poster she presented at the research exhibition show the measured energy in color. The bright red areas, concentrated around the f-holes of the violin, indicate the most intense sound levels. The body gives off pinks and whites. As the map moves away from the violin, the colors turn into a deep blue and then fade to black.
"The data I have so far is only for the A string on one kind of violin," Wang explains. "But now that we know this system works, we can test different strings and different instruments." She continues, "I can use this four planar system on any source. It works well on a violin because of its slightly boxy shape, but it could be anything, even a vacuum cleaner."
"Some people devote their lives to studying the acoustic characteristics of the violin, despite the lack of funding," says Burroughs. "Many people want to know what makes a Stradivarius a Stradivarius."
When Wang and Burroughs finished their violin-playing machine in the spring of 1996, they took it to Carleen Hutchins, a violin maker and a founding member of the Catgut Acoustical Society, an international violin research organization. "Carleen is sort of the grand lady of violins," Wang explains. "She's been studying them for years." The late F.A. Saunders, a physicist at Harvard, founded Catgut with Hutchins in 1963. Its members now include physicists, engineers, chemists, musicologists, performers, com posers, violin makers, and interested laymen. Because Saunders had built a violin-playing machine that he and Hutchins used, Wang wanted to show Hutchins her own version. "We carried it to her home in New Jersey and we had it running in her driveway. People driving by stopped and stared at the weird contraption, sawing away on the violin," says Burroughs.
When a violin is played, whether it's a Stradivarius or a student instrument from a rental shop, both the internal air and the body of the instrument work together to produce the music that we hear. The air inside the instrument has resonances in a lower frequency range, one of these resonances matches the frequency of the D string. The resulting sound is heard through the openings, or f-holes. The body of the violin also has strong resonances that go up into the higher frequency range. One of the strongest matches the frequency of the A string. "This matching of resonance to two major strings may contribute to the violin's beautiful tone," says Wang.
Hutchins has designed and built her own special octet of acoustically matched stringed instruments. Her instruments are structurally different than the traditional violin family Å the violin, viola, cello, and double bass Å and they have artistic possibilities that have only begun to be explored. In every one of Hutchins' octet, the A and D strings are matched to the natural resonances of the instruments. In the regular stringed instrument family, this is only true for the violin. Hutchins has agreed to lend some of her instruments to Wang and Burroughs for testing. Wang is excited Å as soon as her violin-playing machine is ready, she will have it give what might be its most important performance.
"I like the idea of quantifying what makes one violin sound better than another," Wang explains. She pauses. "But in the end, it may just be a subjective, artistic thing."
Lily Wang is a Ph.D. candidate in the graduate program in acoustics, College of Engineering 217 Applied Research Lab, University Park, PA 16802; 814-863-5401; lily@-sabine.acs.psu.edu. Courtney Burroughs, Ph.D., is associate professor of acoustics and senior research associate at the Applied Research Laboratory, 400 Garfield Thomas Water Tunnel; 814-863-3015; cbb@wt.arl.psu.edu. Their research has been funded by the National Science Foundation and by Bell Laboratories.