Ejωt and the time domain in Introductory Engineering Acoustics

Abstract

Introductory classes in engineering acoustics traditionally focus on frequency domain solutions rather than those in the time domain. While this is somewhat historical in nature, it is also true that extensive coverage of analytic techniques for solving space-time partial differential equations is challenging in one semester. This is not a desirable situation because qualitative and quantitative understanding of the link between the frequency and time domains is often elusive to the new learner of acoustics. Such a deficit stands as a barrier to their deep understanding of the material as well as a knowledge gap of ubiquitous and important techniques. Naturally, computational tools to perform these manipulations are available along with high fidelity digital to analog conversion on students’ personal computers. Students now have the capability to play back their simulations to their own ears to compare to experiment. I will present one approach to teaching these concepts to students with no assumed signal processing background using Fourier transforms. I will show how to weave a relatively complicated frequency domain simulation throughout the class and how this model problem can be demonstrated. This same problem also serves to introduce the effects of nonlinear distortion and clipping in transducers.Introductory classes in engineering acoustics traditionally focus on frequency domain solutions rather than those in the time domain. While this is somewhat historical in nature, it is also true that extensive coverage of analytic techniques for solving space-time partial differential equations is challenging in one semester. This is not a desirable situation because qualitative and quantitative understanding of the link between the frequency and time domains is often elusive to the new learner of acoustics. Such a deficit stands as a barrier to their deep understanding of the material as well as a knowledge gap of ubiquitous and important techniques. Naturally, computational tools to perform these manipulations are available along with high fidelity digital to analog conversion on students’ personal computers. Students now have the capability to play back their simulations to their own ears to compare to experiment. I will present one approach to teaching these concepts to students with no assumed signal...