Two waves.
A world of possibilities.
Interference begins with a simple question: what happens when waves overlap? Change their relative phase and discover the answer.
First, make a prediction.
Imagine two sinusoidal waves with equal amplitude, frequency, and propagation direction. When their peaks line up, their displacements add. What happens if the peak of one meets the trough of the other?
A little change. A big difference.
Move the phase slider from 0° to 180°, then continue to 360°. The plot shows a spatial snapshot at a fixed time; amplitudes are normalized.
Resultant amplitude / single-wave amplitude: 1.73
Why does the combined wave disappear at 180°?
At every position, one wave is exactly the negative of the other. Their sum is zero. This idealized model assumes perfectly equal amplitudes and identical frequencies; a mismatch leaves a residual wave.
The mathematics behind the picture.
The magnitude of the combined amplitude is 2|cos(φ/2)| times the amplitude of either wave. It reaches 2 at 0° and 360°, and 0 at 180°. This is a scalar superposition demonstration, not a full electromagnetic simulation.
Read the companion note →Keep exploring in a notebook.
Download the editable Python example and change the phase or amplitudes yourself. Requires a Python environment with NumPy and Matplotlib.
Download the notebook ↓