Independent Study Report: Understanding and Simulating Standing Waves
DOI:
https://doi.org/10.58445/rars.3165Keywords:
Standing Waves, Wave InterferenceAbstract
These working notes study an exploration of standing waves, from basic wave theory to its applications and computational simulations that incorporate realistic noise modeling. The work uses a structured three-phase approach: (1) foundational research, (2) mathematical derivations, and (3) Python-based simulations. The foundational research broadly includes the mathematical principles behind wave interference, how stationary patterns form through superposition, and their importance across multiple areas of science such as musical acoustics, material science (phonons in crystals), quantum mechanics (electron wave functions in atomic orbitals), advanced optics (laser cavity modes and LiDAR), and spectroscopy. Next, the mathematical analysis shows the boundary conditions that govern wave confinement. Finally, we use computational python code enhanced with Gaussian noise to create realistic visualizations that connect theory with physical behavior.
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