Graphic relation between amplitude and sound intensity level

TL;DR

This paper demonstrates through a simple experiment that sound intensity is proportional to the square of amplitude, visually confirming a fundamental wave relationship using common laboratory equipment.

Contribution

It provides an empirical demonstration of the amplitude-intensity relationship in sound waves, which is rarely shown graphically in introductory courses.

Findings

The plot confirms the quadratic relationship between amplitude and sound intensity.

Experimental results align closely with theoretical predictions.

The method is accessible using standard audio and measurement equipment.

Abstract

We present a simple experiment that allows us to demonstrate graphically that the intensity of sound waves is proportional to the square of their amplitude, a result that is theoretically analysed in any introductory wave course but rarely demonstrated empirically. To achieve our goal, we use an audio signal generator that, when connected to a loudspeaker, produces sine waves that can be easily observed and measured using an oscilloscope. The measurements made with these instruments allow us to create a plot of amplitude versus sound intensity level, which verifies the mathematical relationship between amplitude and intensity mentioned above. Among the experimental errors, the plot obtained is in excellent agreement with what is theoretically expected.