Teaching mathematical methods with the help of beer bottles

If you walk into an undergraduate analytical mechanics lab to tables of empty beer bottles, it might not be what it looks like.

Fourier transforms are a mathematical tool for separating a wave into its constituent parts and representing each constituent’s relative contribution. Though commonly used in physics, this concept can be difficult to grasp, so David Kordahl and Emma Foster developed a simple experiment to help students understand the physics of Fourier transforms using the acoustics of bottles.

“The familiarity is key,” said Kordahl. “Students already have a sense for what happens when you blow over a bottle, which gives them an experience as an anchor for the mathematics.”

Instead of blowing into a bottle, their experiments use speakers to vibrate the air above the bottle, causing the air inside the bottle to oscillate. At low frequencies, the speaker’s vibrations and bottle’s oscillations add constructively, but are destructive at higher frequencies. A microphone placed above the bottle picks up on these oscillatory pressures, and by taking two measurements — one of the speakers on their own, and the other of the speakers coupled with the bottle — students can untangle the two signals using Fourier methods and extract the acoustical properties of the bottle.

“Physicists love it when the same basic physics from one system applies to another system,” said Kordahl, noting that the principles the students learn here are also seen in more complex vibrational systems, like charged particles exciting a plasmon.

“I’m interested in how simple classical systems like this one can admit quantum-like descriptions, and how interference effects can be described in complementary ways,” he added. “Introducing these ideas at the undergraduate level seems to me to be increasingly important as we move into the era of quantum technology.”

Source: “Exploring Fourier methods with beer bottles,” by David Kordahl and Emma Foster, American Journal of Physics (2026). The article can be accessed at https://doi.org/10.1119/5.0245272 .