Superposition and interference

Last time

Before we start: last time, in Double slit and the diffraction grating, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

Loud and quiet in one room

Connect two loudspeakers to the same signal and walk across the room. The sound gets louder, then almost vanishes, then loud again. Two waves arrive together and add up, sometimes helping and sometimes cancelling. That is superposition.

Principle of superposition

When two or more waves meet at a point, the resultant displacement is the vector sum of the displacements of the individual waves at that point. Displacements can be positive or negative, so waves can add up or cancel. After they have passed through each other, each wave continues as before. Interference is the effect of superposition when waves from coherent sources overlap, giving a pattern of reinforcement and cancellation.

Constructive and destructive

Constructive interference occurs when the waves arrive in phase, with a phase difference of zero or a multiple of three sixty degrees. The amplitude adds. Destructive interference occurs when the waves arrive in antiphase, one hundred and eighty degrees out of phase. The amplitude subtracts, and is zero if the waves are equal. Two equal waves, constructive: amplitude doubles, so intensity is four times that of one wave. Destructive, equal waves: zero amplitude, zero intensity. Energy is redistributed, not lost.