Instructor: Prof. Changhuei Yang (call me ‘Young’)
Office: 262 Moore
Email: chyang at caltech dot edu
This course is an intuitive introduction to waves. Have you ever wanted to break a wineglass with sound? Or make your own hologram? Or stand under a powerline with a fluorescent light tube? Have you ever wondered what a soliton wave or a vortex is? Come do this and more, as we dissect various types of wave phenomena mathematically and then see them in action with your own experiments. (1-5-0)
What is this course about?
In almost all measurement scenarios, you acquire a signal as it varies across time or space. A microphone picking up sound, for example. Or a photograph (variations of intensity over space).
The way you acquire such a signal and the way you process the signal is a very big part of Electrical Engineering. In this course, you will learn about Fourier analysis – a way in which we can recast time information into the frequency domain and vice versa. In a more basic context, Fourier analysis is one of a much broader class of methods and techniques for transforming information from one basis set to another – an idea that underpins some of the recent exciting scientific advancements, such as machine learning, compressive sensing and big data analysis.
We will discuss and explore a series of important features in Fourier analysis, through the study of waves. Our intention is for you to better appreciate and understand Fourier analysis through a fun experimental context.
In the current COVID pandemic (as of Aug 2020), we have designed and prepared a number of class kits to be mailed to students enrolled in this course (coordinated through the class TA) so that you can conduct the majority of the experiments at home.
Some of the experiments we have lined up include:
Mass-spring wave experiments. Demonstrates the concept of the simple harmonic oscillator (SHO), resonance and mode coupling.
We will also show that a series of coupled simple harmonic oscillators is a medium for wave propagation.
Sound waves and breaking of a wineglass. Explore the idea of a forced simple harmonic oscillator. You will then use the phenomenon of resonance to break a wineglass.
Holography. What is a hologram? Explore the concept of wavefront. You will make your own hologram, and put the hologram under a microscope to see exactly what a hologram is made of.
Soliton. Examine the math behind the soliton phenomenon, and create your own soliton with a rubber band and clothes pins.
Spectroscopy. Construct your own spectrometer and aim it at the sun. We will examine the idea of scattering and the reason behind Los Angeles' spectacular sun rises.
Vortex. Build your own vortex generator and compete with your classmates on setting the longest vortex propagation record. Can you knock over a plastic cup at 1 m, 10 m or 100 m? Explore why vortices can travel far.
This course is made possible by contributions from a group of excellent TAs: Frederic de Goumoens, Cheng Shen, Ruizhi Cao.