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16 March 2015

Two Confusing AP Physics 1 Learning Objectives: Waves

A friend asked about two of the new AP Physics 1 learning objectives.  He's (rightfully) confused about how to present them to his class.  They are:

6.A.4.1: The student is able to explain and/or predict qualitatively how the energy carried by a sound wave relates to the amplitude of the wave, and/or apply this concept to a real-world example.


6.D.4.1: The student is able to challenge with evidence the claim that the wavelengths of standing waves are determined by the frequency of the source regardless of the size of the region. 

I'd say, it's not worth looking this closely at the curriculum framework.  A College Board speaker last year at the AP reading emphasized that straight-up teaching to the learning objectives could lead to disappointment.  She said that a number of teachers to the redesigned biology course had hammered their students with practice tasks and questions narrowly tailored to each learning objective, only to find that the students had trouble handling the broader free response items.

But you have the right general idea about using the curriculum framework to figure out what aspects of waves you need to present to your class.  Try looking not at the learning objectives, but instead at the "essential knowledge" statements.  They state the aspects of each topic that must be covered.  The learning objectives are hyper-specific about skills and "science practices."  Learning objectives are, in my mind, only useful to those asked to write test items; the true outline of the course comes from the essential knowledge statements.  

For the specific topics in your inquiry:

Essential knowledge 6.A.4 merely states the fact that energy carried by a mechanical wave depends on amplitude; and reminds us that examples should include sound waves.  (Not light waves -- that's in AP Physics 2.  We're talking waves on a string, waves in water, sound waves, etc.)  That's easy enough to teach, demonstrate, and explain.  I based a multiple choice question in my book around a stone thrown into a calm pond: the stone creates a wave on the waver's surface.  That wave would carry more energy per meter to a close-by shoreline than a far away shoreline.  And, sure enough, the amplitude of this wave would be higher near the close-by shore than the far away shore.

Essential knowledge 6.D.4 says "The possible wavelengths of a standing wave are determined by the size of the region to which they are confined," which is a highfalutin' way of describing the classic pictures of standing waves.  In language tied to the demonstrations my students have seen, I'd say that the length of a string or pipe must be just right to fit a whole number of standing wave "humps."  This essential knowledge statement goes on to remind us that changing the boundary conditions or the length of the string will change the possible wavelengths.

To me, this just means "teach standing waves."  Now, some folks think of "teaching standing waves" as simply memorizing the equations for fundamental and harmonic frequencies and wavelengths.  No, teaching about standing waves means showing demonstrations and experiments,  It means explaining why standing waves do or do not form.  It means being able to explain with diagrams and words how standing waves in an open pipe differ from those in a pipe closed at one end.  It means relating the relevant equations to those diagrams and words.  

When your students can answer any question about standing waves, including descriptive and experimental questions, you have taught them the necessary background for not just LO 6.D.4.1, but for the AP Physics 1 exam in its entirety.



  1. I'm confused by
    6.D.4.1: The student is able to challenge with evidence the claim that the wavelengths of standing waves are determined by the frequency of the source regardless of the size of the region.

    I thought that the wavelength of a standing wave depends only on frequency and speed of propagation. For most of the simple examples appropriate to Physics 1, speed of propagation is a constant. Or are they expecting coverage of water wave speed dependence on depth? Or are they expecting the Helmholtz corrections to organ pipe lengths for the diameter of the pipe (which really changes the pipe length, not the wavelength)? Under what circumstances does the wavelength of a standing wave change with the size of the region?

  2. Only some frequencies can produce standing waves, is all this is saying. You're right that the wavelength of the standing wave depends on frequency and speed. But if the string isn't an appropriate length, then no standing waves are produced.