The Liberty Bell X-ray and sound wave Letting Freedom ring in a whole new way.

Letting Freedom ring in a whole new way.

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Today, thanks to Gary Koopmann, the Liberty Bell can be heard again. Koopmann, an emeritus distinguished professor of mechanical engineering at Penn State, was director of the University’s Center for Acoustics and Vibrations. One of the classes he taught was called “Designing Quiet Structures.” When it came time to assign an appropriate semester project for his quiet-design students he asked them to recreate, through computer modeling, the most famous American bell of all, Philadelphia’s own Liberty Bell.

We started by defining the overall geometry,” he recounts.  Having established the Bell’s dimensions, its weight (2,080 pounds), and its shape – a traditional English bell profile – they created a structural model, dividing the surface of the bell into a grid made of 450 squares. “There’s an equation describing the vibration of each square, and the computer can solve all the equations simultaneously,” Koopmann says. Then they added an acoustical model, “so we can see a pattern of sound radiation at each frequency.” 

The next step was to add sound. “A bell chord includes five tones,” Koopmann explains. There’s the dominant strike chord, and then there’s a minor third, a major fifth, a nominal, and a hum tone.” They also knew, from published records, what frequencies an English bell would include, and that the Liberty Bell itself had an E-flat strike tone.

Gary H. Koopmann, Ph.D., now retired, was distinguished professor of mechanical engineering and Director of the Center for Acoustics and Vibrations in the College of Engineering, 157A Hammond Bldg., University Park, PA 16802;

Graduate students who worked on the virtual Liberty Bell Project include Dr. Patricia Driesch, Dr. Jeremy Frank, Dr. Michael Yang, Dr. John Fahnline and Ms. Allison Robinson. Dr. Lee Gorny, modified the tone to make it ring several times.

taken from an article by David Pacchioli, the Penn Stater magazine, September 1999.