Exploring Fourier methods with beer bottles

TL;DR

This paper demonstrates how Fourier methods can efficiently model the acoustical resonance of beer bottles as driven-damped oscillators, providing a practical approach for undergraduate experiments.

Contribution

It introduces a Fourier-based technique to quickly extract resonance parameters from beer bottles, simplifying the modeling process for educational purposes.

Findings

Fourier methods enable rapid parameter extraction

Beer bottle resonance modeled as a driven-damped oscillator

Modeling approach suitable for undergraduate labs

Abstract

As anyone who has blown across the mouth of a beer bottle knows, beer bottles have a well-defined fundamental frequency. This paper shows how a beer bottle's acoustical resonance can be modeled as a one-dimensional driven-damped oscillator and includes enough detail to be useful in undergraduate laboratory experiments. While the frequency-domain Green's function of the bottle can be extracted through sequential pure-tone measurements, sufficient data to fit the model's parameters can be collected in just a few seconds when Fourier methods are used.