Simple model of photo acoustic system for greenhouse effect

TL;DR

This paper presents a simple, cost-effective photo acoustic system (PAS) for educational purposes to analyze greenhouse gases' IR absorption, supported by a theoretical model explaining the sound amplitude dependence on IR modulation frequency.

Contribution

It introduces a straightforward theoretical model for PAS that explains the IR absorption measurement without thermal diffusion influence, enhancing educational tools for greenhouse effect studies.

Findings

Sound amplitude depends on IR modulation frequency.

Sound amplitude is unaffected by thermal diffusion.

Experimental results match the theoretical model, including higher harmonics.

Abstract

The green house effect is caused by the gases which absorb infrared ray (IR) emitted by the earth. It is worthwhile if we can adjudicate on which gas causes the greenhouse effect in our class. For this purpose, one of our authors, Kaneko has designed an educational tool for testing greenhouse effect \cite{Kaneko}. This system (hereafter abbreviated PAS) is constructed based on photo acoustic effect. Without difficulty and high cost, we can build PAS and check the IR absorption of gas. In this paper we give the simple theoretical basis for this PAS. The amplitude of sound observed in PAS depends on the modulation frequency of IR pulse. Its dependence can be explained by this simple model. Further we show the sound amplitude does not depend on the thermal diffusion, which provides the accuracy of amplitude as the IR absorption rate of the gas. According to this model, sound signal is not the sinusoidal function and it has higher harmonics. The theory and experiment are compared in the third harmonics by spectrum analysis. From this apparatus and theory, students can study not only the greenhouse effect but also the basics of physics.