Date of Award

Spring 5-17-2020

Document Type

Honors Thesis

Department

Physics

First Advisor

David Jackson

Language

English

Abstract

Acoustic levitation is the phenomenon wherein a standing sound pressure wave can be used to levitate small objects by exerting a force large enough to counter the force of gravity. In this paper we examine the theory of acoustic levitation using an analysis from first-principles, a ponderomotive analysis, and a fluid motion analysis. The first-principles approach involves using Newton’s second law to calculate the net force of an acoustic standing pressure wave on a small object. However, the rapid oscillation of the pressure wave results in a time averaged net force of zero, so we extend the analysis by separating out the rapid motion of the particle from the slow motion. Doing so leads to a ponderomotive force that has a promising form, since the force no longer averages to zero, but disagrees with the research literature. Hence, we consider the accepted analysis using the governing equations of fluid motion and find that the acoustic radiation force causes objects to rest at the pressure nodes of a standing sound pressure wave. The remainder of this paper describes a three-phase investigation into acoustic levitation and schlieren optics. Phase one consists of building a schlieren optics experiment. The schlieren apparatus consists of a point source of light, which is focused by a concave spherical mirror onto a light-block in front of a camera. Changes in refractive index in the path of the light rays will deflect the light rays around the light-block into the camera. This allows for the visualization of minute density gradients in air, allowing us to observe, for example, the airflow above a lit candle or the flow of air from a hair dryer. Phase two of the project involves experimentally producing acoustic levitation. To do this, we use an ultrasonic transducer driven with a 30.1 kHz sinusoidal signal and directed at a flat piece of glass. The resulting standing wave is capable of supporting several small Styrofoam balls. Finally, in phase three we determine the location of these levitating objects using three different analyses: a geometric comparison, direct measurements of the standing pressure wave, and a visual approach using the schlieren system. These three analyses are consistent and demonstrate that objects levitate just below the nodes of standing pressure waves.

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