let freedom ring
What did the Liberty Bell sound like? Science is on the case.
Researchers hunted for clues in modal analysis of 20th-century replica bell at Penn State Behrend.
The Liberty Bell, with its famous crack, hasn’t been rung in 180 years, but that hasn’t stopped scientists from pondering what the bell might have sounded like when tolling. In honor of the nation’s 250th anniversary, researchers at Penn State University have modeled its acoustic properties, drawing on data collected from one of the bell’s replicas. The work was first presented at a meeting of the Acoustical Society of America in Philadelphia earlier this year, followed by an article in Physics Today.
Historians aren’t sure when exactly the Liberty Bell acquired its distinctive crack, just that it occurred sometime between 1817 and 1846. An 1846 account in the Public Ledger described the ringing of the bell on February 23 that year and mentioned that the bell had developed a crack, which someone had attempted to fix by filing the sides down. But it didn’t work: The February 23 ringing extended the crack even more, so much so that “the old Independence Bell… now hangs in the great steeple irreparably cracked and forever dumb.” Nobody has heard it ring since.
This wasn’t the first time the bell had cracked; the rim cracked shortly after it arrived in Philadelphia in 1752, the very first time the clapper struck while testing the sound. It was recast by two local foundry workers, John Pass and John Stow, not once but twice, because the first recast produced a sound that one bystander likened to coal scuttles banging together.
The second recast’s sound was deemed acceptable, and the bell was typically used to summon the Assembly, among other purposes, until it fell into disuse after the American Revolutionary War. As for why the bell was so prone to cracking, a 1975 study of the bell’s chemical composition revealed that the metals used formed “an extremely brittle alloy” that also made it easier for souvenir collectors to chip off pieces from the rim.
Modal frequencies
Seth Collier
Credit:
Seth Collier
We do know something about the general acoustics of bells, dating back at least to a seminal 1987 paper by Thomas D. Rossing and Robert Perrin exploring the forms and vibrational modes of church bells, carillon bells, and handbells. A given bell’s sound is determined by relatively simple geometry—which determines the vibration patterns radiating sound to listeners’ ears—and the material of which it is made (bronze), which determines the exact pitch and duration of the ring.
Per Sean Collier, co-author of this latest article, relying solely on the meager online information about the Liberty Bell to replicate its sound produces “a terrible sounding bell that in presence does not match the silhouette of the iconic bell.” There are several full-size replicas of the Liberty Bell made in the 20th century, including one housed on the Penn State Behrend campus, and one can tap that bell to produce a ring. But scientists desire more quantitative information, such as the specific notes, which notes ring the longest, and how the bell deforms as it vibrates. And that requires modal analysis, a technique used by bell manufacturers to assess tuning and make any necessary corrections.
For instance, Western church bells are typically tuned to the first five normal frequencies, according to the authors—the hum note, fundamental (the note that is most dominant to the human ear), tierce, quint, and nominal—following well-defined ideal ratios. “Musically, the frequencies sound as a minor triad, which is why church bells are commonly perceived as having a somber tone,” they wrote. Furthermore, “The human ear perceives the pitch of a bell as a subjective tone called the strike note,” arising from the combination of how the mode shapes interact, and the listener’s own expectations.
Seth Collier
Credit:
Seth Collier
Collier and his co-authors, Jon Young and Aaron Stearns, decided to use the Penn State Behrend replica to collect their data on mode shapes, natural frequencies, and loss factors. They glued accelerometers to different parts of the replica and then tapped various areas on the bell with a hammer equipped with a force gauge. The accelerators captured the bell’s response to being tapped, and the force gauge measured the force of impact as a function of time.
The authors were then able to extract the bell’s natural vibrational frequencies from that data, along with the corresponding mode shapes and loss factors. The results: The replica’s hum note was 174 Hz; the fundamental was 323 Hz; the tierce was 381 Hz; the quint was 510 Hz; and the nominal was 623 Hz. The ratios of those frequencies fell very close to those of an ideally tuned bell. And the mode shapes of the fundamental frequency closely matched those of typical Western church bells.
Measuring loss factors proved trickiest. Collier et al.’s measured values were within the typical range, but loss factors are impacted by the type of bronze used and casting imperfections. The 20th-century bell-making processes used to cast the replica were different from those in the 18th century used to cast the original Liberty Bell. So the loss factors might have been similar; it’s just harder to predict.
DOI: Physics Today, 2026. 10.1063/pt.103283cd08 (About DOIs).
