Modal frequencies
The replica of the Liberty Bell at Penn State Behrend.
Photo credit: Seth Collier
The replica of the Liberty Bell at Penn State Behrend.
Photo credit: Seth Collier
We know something about the general acoustics of bells, going back at least to a seminal 1987 paper by Thomas D. Rossing and Robert Perrin, in which they examined the shapes and vibration modes of church bells, carillon bells, and handbells. The sound of a particular bell is determined by a relatively simple geometry – which determines the vibration patterns that radiate the sound to the listeners’ ears – and by the material from which it is made (bronze), which determines the exact pitch and duration of the ringing.
Per Sean Collier, co-author of this latest article, relying solely on the sparse online information about the Liberty Bell to recreate its sound results in “a terrible-sounding bell that is inconsistent in its presence with the silhouette of the iconic bell.” There are several full-size replicas of the Liberty Bell from the 20th century, including one on the Penn State Behrend campus, and you can tap this bell to create a sound. But scientists want more quantitative information, such as the specific tones, which tones ring the longest, and how the bell deforms when vibrated. And that requires modal analysis, a technique used by bell makers to assess tuning and make corrections if necessary.
For example, according to the authors, Western church bells are typically tuned to the first five normal frequencies – the hum, the fundamental (the tone most dominant to the human ear), the tone, the fifth and the nominal – following well-defined ideal ratios. “Musically, the frequencies sound like a minor triad, which is why church bells are commonly perceived as a sombre sound,” they wrote. Furthermore, “the human ear perceives the pitch of a bell as a subjective tone called the strike tone,” which results from the combination of the interaction of the mode forms and the listener’s own expectations.
