Week 1: Learning Waves

 Course Description and Goals:

Everything you see is waves. In this course we will study the different types of waves: mechanical and electromagnetic. We will examine the mathematics behind them, as well as construct several different “wave machines” to demonstrate what we have learned. Some days will consist of lecture and planning, while others will be entirely dedicated to building and troubleshooting. Students will be assessed on their understanding of physics and math concepts, as well as their engagement with their engineering projects.

Wave Anatomy

During the first week, our goal was to learn all about waves. This included the different ways we encounter waves (mechanical, electromagnetic, and matter), as well as learning about standing vs. traveling waves.

The first day we learned about the anatomy of a wave - what are its different parts? This includes:

• Amplitude - how far the wave is displaced from its resting point or equilibrium
• Crests and Troughs - these are the points of maximum displacement (positive and negative)
• Wavelength - the distance between two identical points (two crests, for example)
• Period - this is the time it takes for 1 wavelength to pass or the time for one complete cycle of motion
• Frequency - this is the number of wavelengths that pass in each second and also the reciprocal of the Period
• Velocity - in the case of a traveling wave, you can multiply the wavelength and the frequency to calculate the speed (velocity) the wave is moving

Understanding the parts of a wave is fundamental to understanding the physics of waves and how they will behave in the real world. This also lays the grounds for the wave machines we will build and what each machine will demonstrate.

Continuing through the first week, we next learned about Simple Harmonic Motion by discussing the example of a mass-spring system (pictured below) as well as a pendulum.

Mass-Spring system

Moving on, we focused a lot on mechanical waves. These are waves that move through a medium (like ripples on water, or sound waves through air) which is what most of the wave machines will be demonstrating. We discussed the difference between a transverse and a longitudinal waves: transverse waves are vibrating in a direction perpendicular to the direction of motion, while longitudinal waves vibrate in the same direction of motion.

visual of longitudinal and transverse waves

The next concept to discuss that relates to these types of traveling waves, is what happens when two (or more) waves moving through a medium interact? This is the concept of Superposition.

We explored this concept further by creating a double-slit demo to shine a single laser beam through. As the light passes through the slits, it causes the beam to diffract and the pattern is seen on a screen behind. With two slits, the two diffraction patterns will interfere and create points of constructive interference (bright points where crests align) and destructive interference (dark points where the waves cancel out)

diffraction pattern

Continuing with the idea of traveling waves, we next discussed refraction. This is the principle that dictates how a wave travels through a changing medium (for example, from air into water). Put simply, mediums that are harder to travel through (more dense & higher refractive index) will cause the wave to slow down, which can affect both the direction the wave is traveling as well as the wavelength. This can be most easily observed with light bending as it leaves water, as shown below.

Example of Refraction

Finally, we discussed how a standing wave is formed in the context of resonance. This is best discussed through Harmonics. The idea that an object (a string of a given length, or a metal tube) has a "favorite frequency" that when played, will cause the object to vibrate more than at any other frequency. The lowest multiple of that frequency is the "fundamental harmonic". The standing wave consists of nodes (points that vibrate to maximum amplitude) and anti-nodes (points that do not vibrate at all). Higher harmonics can be found by using higher multiples of that fundamental frequency. An example of this on a string is pictured below

This can also be demonstrated using the Rubens Tube we made. The soft membrane at one end of the tube will vibrate at the frequency of the speaker against it creating a longitudinal wave with the gas filling the tube. The wave travels down the tube and reflects off the end, and at the right frequency (again, harmonics!) the returning waves will perfectly align with the waves coming from the membrane and a standing wave is formed. This is visualized by the flames on top, with the higher flames coming at the nodes, as pictured below

Our Rubens Tube in action!