TWO PULSES. ONE RESULTANT.
Wave superposition.
Send two pulses towards each other. At every position, add their displacements.
Watch them meet
ApproachingResultant displacement
Dashed blue · pulse 1 →Dashed gold · pulse 2 ←Solid red · resultant
Contact and overlap buttons pause at that instant.
Pulse 1 · travelling right
Pulse 2 · travelling left
Add the displacements, not the shapes.
Same direction of displacement
Two upward displacements add to a larger upward displacement. Equal, matching pulses give twice the amplitude when their centres align.
Opposite directions of displacement
Upward and downward displacements subtract. Equal, matching pulses on opposite sides cancel completely at full overlap, then reappear as they continue travelling.
Pulse shapes and model
These are finite pulses, not endless wave trains. The sine pulse is a smooth positive half-cycle; the triangle has one peak; the square is rectangular. Width is the total distance from the leading edge to the trailing edge. For the sine pulse, this width is half of its corresponding sinusoidal wavelength, λ = 2w.
Both pulses travel at the same speed through an ideal linear, non-dispersive medium. The sum is calculated at each position; the pulses pass through without reflection or permanent changes. The resultant plot keeps a fixed scale throughout a run. At the ideal square pulse’s instantaneous jumps, plotted values use the midpoint of the two sides.
When widths differ, “Full overlap” aligns their centres: the narrower pulse lies inside the wider one, but complete cancellation requires matching shapes, widths and amplitudes.
Explore superposition and pulse interference
Send two finite pulses in opposite directions through an ideal linear medium. Choose sine, square or triangle shapes independently, change each amplitude and width, and flip either pulse upwards or downwards. Freeze first contact, align the centres for full overlap, or scrub the time slider to inspect the resultant.
Supports wave-superposition topics in IB Physics and A Level Physics, with visual practice in displacement addition and interference for AP Physics. The model adds displacements at every position and shows the pulses continuing unchanged after overlap.