Interference
As a result of superposition, the displacement of the medium at a point is the sum of the displacements due to each wave.
[!abstract] in / out of phase
In phase:
Out of phase:
[!abstract] node / antinode
Locations where amplitude is always zero / maximal
[!abstract]+ nodal / antinodal line
Line of destructive / constructive interference in 2D
- Nodal lines:
- Antinodal lines:
is the same for all points on an antinodal line.
Types
Constructive
Superposition resulting in increased amplitude
Intrinsic phase difference is even multiple of
Destructive
Superposition resulting in decreased amplitude
Intrinsic phase difference is odd multiple of
Partial
Between constructive and destructive
Examples
Two out-of-phase loudspeakers emit 515 Hz sound waves with no time delay. The air conditions on this day are normal. Speaker 1 is at 𝑥 = 1.00 m and speaker 2 at 𝑥 = 3.50 m.
- At the position 𝑥 = 1.25 m, what kind of interference occurs between these two signals?
Destructive interference occurs at that position.
- What is the smallest path-length difference (∆𝑥) that would result in constructive interference?