# Waves LGs: Sp14

These learning goals for Unit 1 of Physics 3 are very similar to the LGs I used last semester. Primarily I tried to add a little more specifics, particularly to the LGs about the derivation, intensity vs. distance, and standing waves. I added a specific LG talking about resonance and clarified and expanded the LGs relating specifically to electromagnetic waves.

I use “Explain” too often in these LGs. I need to sit down with a list of Bloom’s verbs and try to fix this. I also want to sit down and write a few bullet points for each LGs about what specifically it would look like for a student to demonstrate the LG. This should also help improve my verbs. Plus, not every LG can be assessed on an exam (some for practical reasons and others simply due to limited time) so writing these bullet points will force me to plan ahead for LGs that don’t fit into an exam assessment.

**Content Learning Goals**

Upon successful completion of this unit the student will be able to…

1. Explain what does and does not propagate as a wave travels from point A to point B and illustrate this idea by talking about a specific type of mechanical wave. Explain the meaning of wave velocity in light of these ideas.

2. Explain what amplitude, frequency, angular frequency, period, wavelength, angular wave number, phase constant, and wave velocity mean physically and relate these quantities mathematically. The student should know what these quantities mean for both transverse and longitudinal waves and should be able to determine their values given a graph or an equation for a wave function.

3. Write the wave function for a wave traveling in a given direction, at a given speed, with a given amplitude and wavelength. The student can also show that this wave function satisfies the linear wave equation (note that this requires knowing the linear wave equation).

4. Write the wave function for a sinusoidal wave given its graphs (y vs. x and y vs. t) or vice versa.

5. Derive mathematically, along with an accompanying explanation and diagram, one of the following (student’s choice): the linear wave equation for a transverse wave on a string, the speed of a transverse wave on a string, or the speed of a sound wave traveling through a gas. The student should explain and justify any small angle approximations, changes in reference frame, or derivatives used in the derivation.

6. Determine the speed of a wave on a string or the speed of sound through a gas based on properties of the medium. The student can use these results to compare the speeds of waves in different mediums or to compare the speeds of two different waves in the same medium.

7. Define intensity and offer a geometric explanation for how it varies with distance from the wave source in 1D, 2D, and 3D. The student can relate amplitude to intensity and can calculate the amplitude and intensity at different distances from the wave source for water waves, light waves, or sound waves.

8. Explain how decibels relate to sound intensity, and why we use decibels to describe sound intensity. The student can also explain how decibels and intensity relate to loudness and what change in decibels or change in intensity corresponds to a sound “twice as loud”.

9. Explain in words what causes the Doppler effect and what changes (apparent wavelength or apparent speed) when the source is moving compared to when the observer is moving. The student can relate frequencies and speeds mathematically for when the source and/or the observer is moving.

10. Explain the idea of interference or superposition in words and diagrams and given examples of how this phenomenon can be observed in sound waves, water waves, light waves, and waves on a string.

11. Explain the role interference or superposition plays in creating a standing wave and describe the behavior (and physical meaning) of nodes and anti-nodes in a standing wave. Student can also describe the boundary conditions for a standing wave on a string with fixed or free ends and for a standing sound wave in a pipe with open or closed ends as being nodes or anti-nodes. For sound waves, the student can do this for pressure or particle displacement.

12. Sketch a standing wave corresponding to the fundamental frequency or higher harmonics. Student can also calculate the fundamental frequency, harmonic frequencies, and associated wavelengths for a standing wave on a string or in an air-filled pipe.

13. Apply (12) to musical instruments like guitar, flute, or blowing across a Coke bottle to explain how to produce sounds with higher and lower frequencies.

14. Describe the phenomenon of beats and their cause in words. Student can explain the difference between the conditions that create standing waves and the conditions that create beats.

15. Explain the phenomenon of resonance in driven waves and the relationship between resonance, interference, and standing waves. Use these ideas to explain the results of shaking a string with fixed boundary conditions at different frequencies and of striking a tuning fork over tubes of varying lengths.

16. Explain in words the idea of a Fourier series and why it is useful.

17. Explain in words the idea of displacement current and its associated magnetic field.

18. Explain how electromagnetic waves differ from mechanical waves and the role that accelerating charges play in creating EM waves. Student can also mathematically relate the amplitude and phase of the electric and magnetic fields in an EM wave.

It does seem like there’s too many “explain”s in there. And maybe too few “calculates”? One phrase I’ve used to augment “explain” is “I can discuss the foundations of, usefulness of, and ramifications of …” though I think you are being pretty clear about what you want them to explain.

As I read through them, I started thinking about how you might assess a typical homework problem. Here’s an example: An ant is on a string at point x. A wave is sent down the string. Describe the ant’s motion and determine if he is thrown off. That bypasses the “explain” standards a little, though their ability to do the problem would be strongly correlated with them being able to explain things. Does thinking about problems like this help you refine your standards? For me, because of the video standards I do, my students directly tackle the “explain” part, and the dig is that they don’t actually solve problems unless I make it a direct standard.

I like your question, SuperFly. Talking through the ant’s motion would certainly demonstrate a qualitative understanding of some wave aspects and could be made quantitative if we relate it to transverse acceleration for a periodic wave. Thanks.

Wow, this is an impressive list of learning goals. How many weeks do you have for this? Is this the complete list for the course, or is there more to the course?

Quick comments on a few of the specific goals:

3.) & 4.) When you say “wave function” do you mean the differential equation or do you mean the solution to the differential equation?

8.) Decibel is a unit of sound intensity level. Sound intensity level is related to (but not the same as) sound intensity. This is a confusing point for students. I try to be very specific about the distinction so they can think more carefully about what the “level” term means: e.g. sound pressure level, sound intensity level, sound power level, loudness level, etc.

13.) Strictly speaking, blowing across a Coke bottle is an example of driving the Helmholtz resonance of the air cavity. That’s not quite the same as standing waves. See: http://www.phys.unsw.edu.au/jw/Helmholtz.html

15.) Resonance as a concept does not require a wave to be present. Thing of the spring-mass system or pendulum. Those are oscillators which can be driven at resonance (or above or below resonance) but are not wave. This is your only mention of resonance in the learning goals, and although there are mentions of standing waves in other places the connections aren’t obvious here. Also, shaking a string with fixed boundary conditions is an approximation at best, something students should think carefully about. I mean, I have them use the mechanical shakers to drive string oscillations, but we discuss the appropriateness of the boundary conditions that we’re using to analyze the system.

@Andrew, these learning goals are for the first third of the semester. However, the rest of the course continues to focus on waves looking at wave optics and an introduction to quantum mechanics so many of these LGs will be continually revisited throughout the semester.

I am using the phrase wave function to refer to the solution of the differential equation.

Looking at 8) again, you are right that my wording is a little sloppy. I’ve actually not thought about ‘level’ as a general term that could arise in multiple contexts. I’ll have to think more about that idea. Thanks.

I just discovered the UNSW acoustics site. Thank you for pointing me towards the Helmholtz Resonance page. I found last semester that I couldn’t accurately calculate of the frequency produced by blowing across a coke bottle, but I had attributed that to the complicated shape of the bottle not to an incorrect mechanism.

You’re certainly correct that resonance is not solely a wave phenomenon. These students will have had a little exposure to resonance in a mass on a spring and in an LRC circuit in previous semesters. In this class, I’m thinking about the idea of trying to drive a wave at a particular frequency which may or may not correspond to a fundamental or harmonic frequency. There are times when we excite a system with no fixed driving frequency and get a mixture of fundamental and harmonic waves and there are times when we excite a system with a specific driving frequency and either get very little response or a large response at that same frequency. I’m trying to think about how best to present these two scenarios and to what extent I should differentiate them.

Have you checked out this blog?

http://www.wired.com/wiredscience/dotphysics/

I think it’s a blog about physics teaching as well.

Yeah, Dot Physics is a great blog, especially for video analysis ideas. I had forgotten that I don’t have a blog roll anywhere of blogs that I follow. I should put one together. Thanks for the reminder.

This guy’s pretty good too:

http://scienceblogs.com/principles/