Two-source Wave Interference Simulation

A.k.a. "Makin' Waves in Cairo!"

Simulated here is the wave interference pattern produced by two wave sources with identical wavelength lambda.

• A "top-view" 2-D intensity plot is created.
• The plot is square with side length 1000 (arbitrary units).
• The origin is at the center of the left edge of the plot.
• The sources are placed a distance d apart on the left edge of the plot, symmetrically about the origin.

User Inputs

Only these integer inputs for now:

• num_pts = number of points along each axis of the square grid, where 2 <= num_pts <= 25 (max value limited by allowed n_steps on testnet)
• lambda >= 1
• d >= 0

After input, both lambda and d are scaled up to be FP (fixed point) values where FP scale is SCALE_FP = 10**20.

Cairo files

intensity_plot.cairo contains:

• intensity_plot_arr- The view function which accepts user inputs and initiates all calculations
• Other functions to calculate x coordinates, y coordinates, intensities at each position (x, y), and fill arrays for each of these

wave_physics.cairo contains functions for wave physics calculations of:

• Wave function
• Sum of wave functions
• Intensity of combined wave

math.cairo contains math functions to use with fixed point quantities:

• Square root, multiplication, division
• Distance between two points
• Shift any angle theta to equivalent angle theta_shifted within range -pi to pi
• Cosine approximation using Taylor series, requires -pi <= angle <= pi

structs.cairo contains struct definitions for:

• Wave parameters common to both sources
• Wave parameters for an individual source
• Combined parameters for two waves

constants.cairo contains:

• FP math constants
• Other math constants
• Physical wave parameters (except those that are user inputs)
• Plot parameters (except those that are user inputs)

Tests

test_intensity_plot.py

• Contains input parameters which are fed into both Cairo and Python calculations
• Contains other constants and parameters (that should match those in constants.cairo) for Python calculations
• Contains Python calculations of intensity array, to compare to Cairo calculations done by calling intensity_plot_arr function from intensity_plot.cairo using same input parameters
• Dumps intensity_plot_arr return to test_intensity_plot.json to be used by Jupyter notebook
• Prints for comparison the values (as FP) from the intensity arrays found with Cairo and Python
• To run: pytest -s tests/test_intensity_plot.py

test_intensity_plot.ipynb

• Jupyter notebook which plots two intensity arrays:
  • Array calculated in Cairo by intensity_plot.cairo
  • Array calculated in Python by test_intensity_plot.py
• Gets data from .json files created in test_intensity_plot.py
• To run:
  • Install Jupyter Notebook
  • jupyter notebook, follow instructions to open notebook in browser
  • Open file test_intensity_plot.ipynb

test_math.py

• Compares Python calculations to those found by calling theta_shifter and cosine_8th functions from math.cairo
• Note:
  • n = 5 is used to include 5 terms (to 8th order) in Python cosine approximation, to match approximation in cosine_8th function in math.cairo
  • num_tests = an odd integer number of tests to run
  • Values of theta to test are incremented by pi/4 in range: -(pi/4)(num_tests-1)/2 <= theta <= +(pi/4)(num_tests-1)/2
• To run: pytest -s tests/test_math.py

License

This repository is licensed under the MIT license.