Modeling and visualization of linear superposition of sine waves and resultant interference patterns

• Python 3.11.4
• Matplotlib 3.7.2
• Seaborn 0.12.2
• NumPy 1.25.2

• Standalone Module
• IPython Notebook / Jupyter Notebook

• Wave equation
• Superposition principle

• Wave model parameters
• Superposition plot parameters

• Modeling of sine wave superposition phenomena and interference patterns

The sine wave equation in one-dimension can be represented as:

$y(x, t) = A \sin(kx \pm \omega t + \phi)$

where:

$y(x,t)$ is the wave displacement at position $x$ and time $t$
$A$ is the amplitude
$k = \frac{2\pi}{\lambda}$ is the wave number
$\omega = 2\pi f$ is the angular frequency
$\phi$ is the phase offset
$+$ or $−$ depends on the direction of propagation (right or left)

The superposition principle states that when two or more waves overlap in space, the resultant wave is the algebraic sum of their individual waves. When two waves $W_1$ and $W_2$ interfere, the resultant wave $W_R$ can be given by:

$W_R(x, t) = W_1(x, t) + W_2(x, t)$

Interference patterns are the result of the superposition of two or more waves. These patterns can be either constructive or destructive depending on the phase and amplitude of the interacting waves.

These patterns can display areas of both constructive and destructive interference, and they are commonly seen in phenomena like double-slit experiments and sound wave interference.

model_sinewave() function

These parameters can be used to represent the waves in the model:

$\large y(x, t) = A \sin\left( \frac{2\pi}{\text{wavelength}} \cdot x \pm 2\pi \cdot \text{frequency} \cdot t + \phi \right)$

plot_wave_superposition() function