This lecture is about wavefronts, which is a very specific way that we represent
the movement of waves. So a wavefront is the set of all locations in a medium
where the wave is at the same phase. This could be where all the crests are, where
all the troughs are, or any phase in between. Wavefronts are useful for
showing how waves move in two dimensions. The length between two lines on a
wavefront is exactly one wavelength, and that makes sense because they're where the
same phase occurs. So any two places where the same phase occurs, the distance
between those will be one wavelength. As an example we could pretend that this
wave is moving through water, and I'm trying my best to represent this wave in
2D like we're looking down at the water, like it's a pool or something like that,
and we can see where the high points and low points of the water are. But this is
a very inexact way of measuring those high points and low points, so instead
we're going to draw this as a wavefront. To draw this as a wavefront I'm going to
draw a line where all the crests of each wave appear. So those lines are an
example of a wavefront, this very specific way of representing where waves
are in a medium. And obviously the distance between two lines on a
wavefront is one wavelength. So this is what the wavefront would look like by
itself if you encountered it in a problem or a test, just these lines. And
you know that at each point, and you know that at each line that's where the same
phase of the wave occurs. So the distance between those two lines is one
wavelength. We could also draw the wave fronts where the troughs of the wave
appear, and in that case this would still be the wavelength, just shifted a little
bit, but besides that it's the same wave. We could also draw them like this
between the trough and the crest, and again this is the same wavelength just
shifted a little bit. Wavefronts can come in different shapes depending on
the movement of the wave, so the one I drew on the left could be waves moving
from left to right or right to left. I just indicated that their velocity is to
the right. The other picture shows waves moving outward in all directions
so the second example would be like if you dropped a stone into a pond and
observe the waves moving out. Wavefronts can show where constructive and
destructive interference of waves will occur. When two waves are perfectly in
phase they experience constructive interference, and when two waves are
perfectly out of phase the experienced destructive interference. So as an
example I have a red and a blue wave and and above them I have an image of the
wavefronts of the wave. Just imagining that we're looking straight down at
these waves as they move through a material. So when the lines of the wave fronts are exactly between each other that's when destructive interference
occurs, because you can see that each trough of the blue wave is lining up
with each crest of the red wave, which will cancel out the total wave and
become zero altogether. So that's where perfectly destructive interference
occurs, where the two wavefronts are in between each other. Constructive
interference occurs when they perfectly line up, because you can see here the
crests are above other crests, the troughs are above other troughs, so if
the lines of the wavefronts occupy the same place that's where constructive
interference occurs. This is going to matter a lot for understanding how waves
expand and interact with other expanding waves. As an example we could imagine
that we drop two rocks into a pond at different points and two waves start to
expand out in all directions from each. One l'll label as red and the other is blue,
and you can see that as they expand out they're going to start to interact with
each other, and we're going to want to know where constructive and destructive
interference occurs, where they're interacting. I'm going to put a green dot
wherever constructive interference occurs, and that's basically going to be
anywhere where we have two overlapping lines. Whenever two lines are in the same
place, that means the same phase of the wave is in the same place, so this is all
the places where constructive interference will occur between these
two waves. Destructive interference will occur where the line of one wave is
exactly in the middle of the lines of two other waves.
So that'll be all these red positions right here, and you can see that this
pattern is formed when we actually do oscillate two objects in water. It's
a little difficult to see what's happening in the middle of the two
things he's oscillating in the water, but something like that pattern is going to
occur, and as the wave spread out you can see that there are certain places where
there's constructive interference which I've labeled in green and destructive
interference which I've labeled with red. So one more time you can see
constructive interference where there are very large wave crests and
destructive interference where there's nothing. And that's what you need to know
about how to label wave fronts.