Why do double-walled bottles have a second resonance?

Many improvising musicians have created an impromptu instrument from a collection of glass bottles. Blowing air across the top of one of these bottles produces a note, which can be modulated by partially filling the bottle with water. This is an example of Helmholtz resonance, one of the two types of acoustic resonance that can be demonstrated with a bottle.

Daniel Ludwigsen and Alexandria Meade designed a classroom experiment to teach students about resonance using double-walled insulated bottles. Their goal was to provide a way for students to investigate complex problems involving resonance and oscillation using a familiar object.

While Helmholtz resonance is often demonstrated using single-walled bottles, double-walled bottles also exhibit the second kind of resonance, which occurs when striking the side wall of such a bottle. The inner and outer walls then oscillate opposite one another.

“The structural resonance arises from the inner and outer walls of the bottle, coupled by the stiffness provided by their connection at the neck,” said Ludwigsen. “This is tied explicitly to the oscillation of the bottle’s structure.”

When performing this experiment, students may discover that adding water to the bottle adjusts the pitch of the two resonances in opposite directions, meaning it may be possible to get the resonances to overlap or to experience a beat frequency.

The authors hope this classroom activity will help to engage students with physics concepts.

“It’s always great to be able to bring everyday objects into the labs,” said Ludwigsen. “Many of our students come to physics or engineering with a background in music, so we’re always looking to develop ideas related to sound.”

Source: “Two oscillators in the double-wall bottle,” by Daniel O. Ludwigsen and Alexandria Meade, American Journal of Physics (2026). The article can be accessed at https://doi.org/10.1119/5.0304544 .