The effect of liquid on the vibrational intensity of a wineglass at steady state resonance

TL;DR

This paper investigates how adding liquid to a wineglass lowers its natural frequency and resonance intensity, combining theoretical modeling with experiments to analyze the relationship and limitations of the model.

Contribution

It extends existing research by linking pitch lowering to resonance intensity reduction and proposes a theoretical model validated by experimental data.

Findings

Resonance intensity is proportional to the square of natural frequency.

Damping coefficient increases with more liquid, affecting model accuracy.

Theoretical model aligns with experiments when damping is constant.

Abstract

As a liquid is inserted into a wineglass, the natural frequency of the wineglass decreases. This phenomenon, known as pitch lowering, is well explained in past papers. However, previous literature have not yet mentioned that pitch lowering also reduces the resonance intensity of a wineglass. Thus, this present paper aims to extend the body of research on this topic by describing the relationship between pitch lowering and its effect on resonation intensity. To do so, we identify the vibrating wineglass wall as a damped harmonic oscillator, derive a theoretical model, and find that the resonance intensity of the wineglass is proportional to the square of its natural frequency, under the assumption that damping stays constant. However, our experiments showed the coefficient of damping to increase with respect to the amount of liquid, which caused the data to deviate from its theoretical predictions. We conclude by discussing the accuracy and limitation of our proposed model.