Babinet's principle in the Fresnel regime studied using ultrasound

TL;DR

This study investigates ultrasound diffraction by a circular disk and aperture to demonstrate Babinet's principle in the Fresnel regime, confirming the principle and exploring phase relationships with a simple graphical method.

Contribution

It provides experimental verification of Babinet's principle in ultrasound diffraction and introduces a straightforward graphical analysis approach.

Findings

Babinet's principle is verified in the ultrasonic Fresnel diffraction regime.

The incident wave phase is found to lag 90 degrees behind the wave passing through the aperture.

The apparatus serves as an educational tool for demonstrating wave diffraction phenomena.

Abstract

The diffraction of ultrasound by a circular disk and an aperture of the same size have been investigated as a demonstration of Babinet's principle in the Fresnel regime. The amplitude and the phase of diffracted ultrasonic waves have been measured, and a graphical treatment of the results is performed by simply drawing vectors (phasors) in the complex plane. The results verify Babinet's principle. It is also found that the incident wave is indeed 90 deg behind the phase of the wave passing through on the central axis of a circular aperture. This paradox has previously been regarded as a defect of Fresnel's theory. The apparatus used is intended as a table-top instrument for the student laboratory in general science and engineering classes.