What Did the Sound of the Liberty Bell Sound Like? Science Has the Answer.
Researchers searched for clues in a modal analysis of a 20th-century replica bell in Pennsylvania.
Researchers looked for clues in a modal analysis of a 20th-century bell replica at Penn State.
Liberty Bell outside Independence Hall in Philadelphia
The Liberty Bell, with its famous crack, hasn't been rung in 180 years, but that hasn't stopped scientists from wondering what it sounds like when it rings. In honor of the country's 250th anniversary, Penn State University researchers have modeled its acoustic properties using data collected from one of the bell's replicas. The work was first presented earlier this year at the Acoustical Society of America meeting in Philadelphia, followed by an article in Physics Today.
Historians aren't sure exactly when the Liberty Bell acquired its distinctive notch, but it's only been between 1817 and 1846. An 1846 report in the General Office mentions the ringing of the bell on 23 February of that year, noting that it had developed a crack, which someone had tried to fix by filling it. But it didn't work: the ringing of February 23 widened the gap even further, so that "the old Independence Bell ... now hangs in the Great Tower, irreparably cracked and forever dumb." No one has heard its bell since.
This was not the first time the bell was broken. The rim cracked shortly after arriving in Philadelphia in 1752, the first time Clapper struck when testing sound. It was rewritten by two local foundry workers, John Pass and John Stowe, not once but twice, as the first rewrite produced a sound that an audience member likened to the pounding of coal stones.
The sound of the second version was considered acceptable, and the bell was commonly used to summon assemblies, among other purposes, until it fell into disuse after the American Revolutionary War. As for why the rust was so prone to cracking, a 1975 study of the chemical composition of the rust found that the metals used formed a "highly brittle alloy" that made it easier for souvenir collectors to separate pieces from the rim.
We know something about the general acoustics of bells going back at least to an important 1987 paper by Thomas D. Rossing and Robert Perrin, who investigated the shapes and modes of vibration of church bells, carillon bells, and handbells. The pitch of a given bell is determined by the relatively simple geometry—that is, the vibration patterns that radiate the sound to the listeners' ears—and the material it is made of (bronze), which determines the exact pitch and duration of the ring.
Per Sean Collier, one of the authors of this latest article, relying only on the scant online information about the Liberty Bell to replicate its sound, "the bell produces a terrifying sound that does not match the iconic bell's specter in presence." There are several full-size replicas of the Liberty Bell made in the 20th century, including one on Penn State Behrend's campus, that you can strike. That bell is designed to produce a ring, but scientists want a little more information, such as the specific notes, the notes that ring the longest, and how the bell changes shape when it vibrates. And that requires modal analysis, a technique used by bell makers to evaluate tuning and make any necessary adjustments.
For example, according to the authors, Western church bells are typically tuned to the first five common frequencies—home note, fundamental (the note most dominant to the human ear), row, toe, and nominal—following well-defined ideal ratios. "Musically, frequencies sound like a minor triplet, which is why church bells usually have a sad sound," they wrote. In addition, "the human ear perceives the sound of a bell as a subjective tone called a percussive note," which results from a combination of how mood shapes interact and the listener's own expectations.
Collier and his colleagues, 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 attached accelerometers to various parts of the mockup and then tapped different areas on the bell with a dynamometer-equipped hammer. The accelerometers received the bell-to-impact response, and the dynamometer measured the impact force as a function of time.
Then the authors were able to extract the natural vibrational frequencies of the bell along with the corresponding data. Mode shape and loss factors Results: The sound of the home mock was 174 Hz. The fundamental was 323 Hz. The row was 381 Hz. Quint was 510 Hz. and nominal was 623 Hz. The ratio of these frequencies was set very close to the ratios of an ideal bell. And the fundamental frequency mode shapes corresponded to typical western church bells.
Loss factors were more difficult to measure. The values measured by Collier et al were within the normal range, but loss factors are influenced by the type of bronze used and casting defects. The 20th century bell-making processes used to cast the replica differed from those used in the 18th century to cast the original Liberty Bell. So the loss factors may be similar. It's just harder to predict
DOI: Physics Today, 2026. 10.1063/pt.103283cd08 (About DOIs).
Jennifer is a senior writer at Ars Technica with a special focus on the intersection of science and culture, covering everything from physics and related interdisciplinary topics to her favorite movies and TV series. Jennifer with her husband, physicist Sean M. Carol, and their two cats, Ariel and Caliban, live in Baltimore.