This document discusses 2D wave interference. It explains that in 3D waves propagate in different orientations resulting in varying phase differences based on position, unlike 1D waves where phase does not change with time or position. Constructive interference occurs when waves are in phase at a point, while destructive interference is when one wave is positive and the other negative at a point. For two spherical waves, the path difference between sources and a point of interference must be an integer multiple of the wavelength for constructive interference or half-integer multiple for destructive interference. The document provides an example where the path difference between sources for destructive interference at a speaker is half a wavelength.

1. 2D Wave Interference
By Xinqi Shao (40497133)
Physics 101 202, section LE2

2. Interference
 In the situation of 3D waves, waves propagate in
different orientations and their relative phase will be
different with their positions. This is different from the
propagation of one dimensional waves, in which the
phase difference will not be different with time or
position.

3. According to the picture shown below, the black circles
show where the waves are in phase, leading to
constructive interference, and the open circles shows the
two waves are out of phase, resulting destructive phase.

4. If a point where two waves are interfering
constructively, then both waves must be at their peak
positive (or negative) amplitude at the point.

5. According to Figure 15-15, we can find that there is an
integer number of wavelengths between each of the
sources and the intersection point. We can therefore
develop the following equation, 15-16, which expands
further to 15-17:

6. For the propagation of two spherical waves travelling
away from their sources, the wave fronts move over a
large area. The cosine functions for each wave differ by
an integer multiple of 2pi

8. Destructive interference occurs when a point at which the
wave from one source is at a positive amplitude while the
other source is at a large negative amplitude.
Mathematically, the path difference is a half-integer
multiple of the wavelength for the two waves.

9. Try it
How far should source 2 be away from source 1 in order
to completely cancel out the wave at the speaker?
A. 2λ
B. λ
C. λ/2
D. λ/4

10. Answer
Cancelling out the wave at the speaker, destructive
interference must be formed. We know that to form
destructive interference we must a half-integer multiple of λ,
we can therefore eliminate A, B, and D, choosing C.

11. Thanks for watching 