Principle of superposition
● VERBATIM — examined word-for-wordWhen two or more waves of the same kind meet at a point, the resultant displacement at that point is the vector sum of the individual displacements that each wave would produce at that point on its own.
y = y₁ + y₂ + y₃ + … (displacements added with their signs)What this actually means
The mark-earning word is displacement. Not amplitude, not intensity, not energy. If wave 1 gives +3 mm and wave 2 gives −5 mm at that instant, the resultant is −2 mm. Signs are the whole point.
Same kind matters. Sound superposes with sound, light with light, water ripples with water ripples. A sound wave and a light wave crossing at the same point do absolutely nothing to each other.
It is a point-by-point, instant-by-instant rule. You apply it at one position at one moment. To draw a whole resultant waveform you repeat the addition at every position along the axis.
In sketch questions, do not eyeball an average. Pick the easy positions first (where one wave is zero, where a crest sits on a crest, where a crest sits on a trough), add the ordinates there, then join them smoothly.
Everything later in this topic is this single rule in different geometries. Stationary waves are superposition of two opposite-travelling waves. Interference is superposition of coherent sources. Single-slit diffraction is superposition of Huygens wavelets. Nothing new gets bolted on.
Adding amplitudes instead of instantaneous displacements, so you claim 2A everywhere instead of a resultant that varies with position and time.
Prove it — watch it be true
- Set the mode selector to two pulses and launch them towards each other.
- Pause at the frame where they half overlap and read the resultant trace against the two individual traces.
- Check by hand that the resultant ordinate at any x equals the sum of the two dashed ordinates, signs included.