Thermal physics provided the transition from macroscopic physics to microscopic physics, and electricity is all about electrons, so why are we backtracking now to talk about bouncing springs and wiggling strings?
It’s because waves are going to be essential, ultimately, to our understanding of the inner workings of the atom. Bohr’s earliest thoughts about the atom involved viewing electrons as little mass/spring systems – “harmonic oscillators” – inside the atom. Later he would switch to a model in which the electrons orbit the nucleus. Orbits are circular motion, and circular motion is intimately related to simple harmonic motion. It all ties together!
Key Points for IB Students
- F = -kx or a = -kx are the defining equations of simple harmonic motion. Make sure you know what these graphs look like (straight line, negative slope, through origin)
- Sound is a longitudinal wave
- Electromagnetic waves (light) are the only type that need no medium.
- Light must be a transverse wave, because we can polarize it
- Know how to derive velocity = frequency * wavelength
- Be sure you understand transverse and longitudinal waves
- Be able to use and sketch graphs of displacement vs time AND displacement vs position. From a graph of displacement vs position, you can get wavelength but not period. From a graph vs time you can get period but not wavelength. This is a common source of trouble for students.
- A graph of displacement vs time or position looks the same regardless of whether the wave is transverse or longitudinal. It’s only the direction of the displacement that is different. For transverse, displacement is perpendicular to the direction the wave moves. For longitudinal, displacement is parallel to direction of travel of the wave.
- Energy of a wave is proportional to square of amplitude (because energy in SHM is proportional to square of displacement, as we see in energy of a spring = 1/2kx^2)
Oscillations and Simple Harmonic Motion (4.1)
Did you ever wonder why pi shows up in so many places where you might not expect it? One reason is that simple harmonic motion is related to circular motion. Pi is not just about circles, it’s about oscillations, and oscillations are everywhere, so pi is everywhere.
- Mass and spring with graphs – http://www.geogebratube.org/student/m2224
- SHM and circular motion – http://www.geogebratube.org/student/m42907
- Pendulum simulator – http://phet.colorado.edu/sims/pendulum-lab/pendulum-lab_en.html
- Mass and spring simulator – http://phet.colorado.edu/sims/mass-spring-lab/mass-spring-lab_en.html
Watch the following video!
- SHM – https://archive.org/details/AP_Physics_B_Lesson_16
- Mass and spring systems – https://archive.org/details/AP_Physics_B_Lesson_17
- Analyzing pendulum motion – https://archive.org/details/AP_Physics_B_Lesson_18
Traveling Waves (4.2)
- Wave on a String simulator – http://phet.colorado.edu/en/simulation/wave-on-a-string
- Longitudinal Wave animation http://www.geogebratube.org/student/m4584
- Wave graphs vs distance and time http://www.acs.psu.edu/drussell/Demos/wave-x-t/wave-x-t.html
Wave Characteristics (4.3)
This simulation can help you visualize wavefronts: http://phet.colorado.edu/en/simulation/wave-interference
Simulator for polarized light passing through polarized film: http://tutor-homework.com/Physics_Help/polarized_light.html
Watch this Youtube video showing use of polarized light to identify stress in molded plastic
Good animation of superposition of waves http://www.acs.psu.edu/drussell/Demos/superposition/superposition.html
Wave Behavior (4.4)
Simulator for refraction, critical angle, and total internal reflection: http://phet.colorado.edu/en/simulation/bending-light
- Single slit diffraction simulator This sim allows you to see how slit width and wavelength affect the diffraction pattern: http://www.walter-fendt.de/ph14e/singleslit.htm
- Double slit diffraction demonstration by Veritasium. Real life demonstration of Young’s famous experiment that “proved” light is a wave
- Double slit diffraction and interference simulator Use the “Light” tab and click on “Intensity Graph” to be able to see a graph of the diffraction pattern. http://phet.colorado.edu/en/simulation/wave-interference
- Double source interference simulator. This is not an example of diffraction but it does give you a very good picture of what the interference pattern looks like when you have two sources of waves (Since slits are like independent sources, this is the same pattern you get when studying double slit diffraction) http://phet.colorado.edu/en/simulation/sound
Standing Waves (4.5)
Wave on string demo showing multiple harmonics with a vibrating string
a) Understanding standing waves as superposed reflections: http://www.acs.psu.edu/drussell/Demos/superposition/superposition.html
b) Longitudinal waves in pipes
Measuring speed of sound using standing waves
Famous video of Tacoma Narrows bridge collapse video
Millenium bridge resonates shortly after opening