Harmonic Wave Simulator
Adjust amplitude, frequency, and wavelength in real time. Visualize oscillating particles, inspect derived wave quantities, and enable a second wave to explore constructive and destructive interference.
Harmonic Sine Wave Simulation
y(x, t) = A · sin(2π(x/λ - f·t))
What to observe
At constant wavelength, raising frequency increases the displayed propagation speed. Amplitude changes displacement, not frequency.
Superposition
Enable the second wave and compare its dashed trace with the resultant wave to see interference evolve over time.
Model scope
Canvas distances are illustrative pixels. Use the universal calculator for physical units and real media.
Three experiments to try
- Change amplitude only. Keep frequency and wavelength fixed, then raise amplitude. The crests become taller while their spacing and travel speed remain unchanged. A particle moves around its equilibrium position rather than traveling along with a crest.
- Compare frequency and wavelength. Start at 1 Hz and a wavelength of 180 px: v = 180 px/s. At 2 Hz with the same wavelength, v = 360 px/s. To represent the original speed at 2 Hz, reduce wavelength to 90 px. In a fixed, nondispersive physical medium, speed constrains frequency and wavelength; this sandbox lets you vary them independently.
- Enable 2-Wave Superposition. Match the two frequencies, then change the second amplitude. Compare the individual traces with their sum: displacements reinforce when they have the same sign and partly cancel when they have opposite signs. Different frequencies make the interference pattern change over time.
The model uses y = A sin(2π(x/λ − ft)). A is displacement amplitude, λ is wavelength, f is frequency, x is position and t is time. The minus sign describes motion in the positive x direction. It models a transverse displacement; sound in air is longitudinal, although the same frequency–wavelength relationship applies.
Read more about wave speed, amplitude and period in OpenStax.
Harmonic wave questions
What does a harmonic wave simulator show?
It shows a sinusoidal traveling wave. Amplitude sets the maximum displacement, wavelength is the distance between successive crests, and frequency is the number of oscillations per second. The displayed wave speed is their product.
Does increasing amplitude make this wave travel faster?
No. In this linear model, amplitude changes displacement but does not enter v = fλ. With frequency and wavelength unchanged, the wave speed stays the same.
Are the distances in the simulator measured in meters?
No. Amplitude and wavelength are illustrative pixel distances, so the displayed propagation speed is in pixels per second. Use the wavelength and frequency calculator for physical units and medium-specific speeds.