I was asked about standing waves in pipes on the AP Physics 1 exam. Specifically, is it important for students to understand the difference between a variation in air pressure, and a variation in the amplitude of particle displacement?
On one hand, it is certainly important to understand nodes and antinodes in closed and open pipes. When the boundary conditions are the same (closed at both ends, open at both ends) the fundamental frequency is v/2L and all multiples of the fundamental frequency can be played; when the boundary conditions are different (open at one end and closed at the other), the fundamental frequency is v/4L with only odd multiples available.
Then, we have to understand the WHY behind these facts. Students must be able to draw pictures of standing waves, must be able to identify the wavelength as it relates to a picture of standing waves and as it relates to a pipe length, understand why the speed of waves is constant, how the wave speed relates to the speed of particles in the material, how the particles actually move in a transverse wave and how that relates to the pictures and to the wave's amplitude. (Whew.)
But, when drawing standing waves, are we drawing a representation of the air pressure or the particle displacement? And, does it matter?
Any time you're wondering about what will be tested on an AP exam, be as a biblical fundamentalist: ignore peoples' pronouncements and go straight to the source text.
I've just been through four released AP Physics 1 exams. Not a single question addressed the difference between air pressure and particle displacement. Now, that doesn't mean a question next year or the year after couldn't do so, because the AP Physics 1 exam is only a few years old.
Nevertheless, I'm taking a Bayesian approach. The difference between particle displacement- and air pressure- representation is extraordinarily abstract, and difficult to understand for a student who hasn't studied fluids, anyway. The mathematics and representations of standing waves work fine even if students don't know what exactly they're representing. Therefore, I don't address this issue of pressure vs. particle displacement.
If that means my students have to guess on one multiple choice question every half-decade, that's a price I'm definitely willing to pay for simplifying their understanding of standing waves in a pipe.