Welcome to FS/EE 005 Introduction to Waves (Spring 2021)

Course Information

Instructor: Prof. Changhuei Yang (call me ‘Young’)
Office: 262 Moore
Telephone: 626-395-8922
Email: chyang at caltech dot edu

Course Description

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.

Figure 1 – Mass-Spring Experiment. Left: Two coupled SHO built using the experiment kit. Right: MATLAB tracking of the mass position.

We will also show that a series of coupled simple harmonic oscillators is a medium for wave propagation.

Figure 2 - Twenty coupled SHO setup, allowing us to see a wave propagating.

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.

Figure 3 – Soundproof box equipped with two speakers and a highspeed camera to record the motion/breaking of 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.

Figure 4 - The hologram experiment. Left: the toy car that we used for making the hologram. Right: when we move the car away and only shine a laser on the finished hologram, a 3D image of the car appears.

Soliton. Examine the math behind the soliton phenomenon, and create your own soliton with a rubber band and clothes pins.

Figure 5 - The soliton experiment. Left: the soliton band made of an elastic rope and clothes pins. Right: when we twist one end of this band and release, the solitoin wave will propagate to the other end (adapted from https://vimeo.com/21661807).

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.

Figure 6 - The home-made spectrometer experiment. Left: a pinhole camera made of carton or shoebox and cell phone with a diffraction grating plate behind the aperture. Right: the image taken by the cell phone where you can see the sunlight spectrum at the first order diffraction.

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.

Figure 7 - Schematics of a generic homemade vortex generator.

This course is made possible by contributions from a group of excellent TAs: Frederic de Goumoens, Cheng Shen, Ruizhi Cao.