SPRDSenior Physics Research DatabaseDickinson College

All projectsDirectional speaker

Analysis

Simulation against measurement

Run the AM version of the KZK model with the real speaker's parameters and compare it, curve by curve, with your recordings.

Weeks 3–4 of 4; the paper is due at the end of week 4

Goals

  • Run `kzk_sim.py --am` with the speaker's carrier frequency and size and the room's temperature and humidity.
  • Overlay the simulated and measured 1 kHz level against distance, and compare the distortion.
  • Explain every disagreement either quantitatively or as a clearly stated limitation.

Why this matters

This comparison is the Discussion of your paper. Agreement shows you understand the physics. A disagreement you can explain is just as valuable.

The physics

The main sources of mismatch are known in advance. Listing them before you look at the data keeps you honest:

  • Geometry. The code models a 2D strip source, whose beam spreads as z−1/2z^{-1/2}; a real panel spreads as z−1z^{-1}.
  • Carrier level. You probably don’t know the speaker’s carrier amplitude p0p_0, and the audio scales as p02p_0^2.
  • Modulation. The simulation uses plain AM. If the speaker preprocesses its signal, it will distort less than the simulation predicts.
  • Room. Reflections are not in the model at all.

Hints

Hint 1Fix one unknown with one measurement

Choose p0p_0 so the simulated 1 kHz level matches your measurement at one distance, then see whether the other distances agree. One fitted parameter tested against many points is a real test. Fitting everything is not.

Hint 2Compare shapes before levels

Normalise both curves to their maximum and compare shapes first, then absolute levels. Shape and level fail for different reasons.

Hint 3Distortion is a sharp test

The simulated THD depends on the modulation scheme much more than the level does. If the measured THD is far lower than the plain-AM prediction, that is evidence the speaker preprocesses its input.

Hint 4Write the limitations paragraph now

Draft the paragraph on the model’s limits while running the comparison, not the night before the paper is due.

What past teams did

2026–27 team

First team on the project. Add the comparison plots and the parameter set you used.