WAVE INTERFERENCE

What happens when two waves meet while they
travel through the same medium? What affect
will the meeting of the waves have upon the
appearance of the medium? Will the two waves
bounce off each other upon meeting (much like
two billiard balls would) or will the two waves
pass through each other?

Wave interference is the phenomenon that
occurs when two waves meet while traveling
along the same medium.

The interference of waves causes the medium to
take on a shape that results from the net effect of
the two individual waves upon the particles of
the medium.
Consider two pulses of the same amplitude
traveling in different directions along the same
medium. Let's suppose that each displaced
upward 1 unit at its crest. As the pulses move
towards each other, there will eventually be a
moment in time when they are completely
overlapped.
 At that moment, the resulting shape of the
medium would be an upward displaced pulse
with an amplitude of 2 units.



Constructive interference is a type of
interference that occurs at any location along the
medium where the two interfering waves have a
displacement in the same direction.
In this case, both waves have an upward
displacement; consequently, the medium has an
upward displacement that is greater than the
displacement of the two interfering pulses.
Constructive interference is observed at any
location where the two interfering waves are
displaced upward.
 But it is also observed when both interfering
waves are displaced downward.

INTERFERENCE

Destructive interference is a type of
interference that occurs at any location along the
medium where the two interfering waves have a
displacement in the opposite direction.

At the instant of complete overlap, there is no resulting
displacement of the particles of the medium. This
"destruction" is not a permanent condition. In fact, to say
that the two waves destroy each other can be partially
misleading. When it is said that the two pulses destroy each
other, what is meant is that when overlapped, the affect of
one of the pulses on the displacement of a given particle of
the medium is destroyed or cancelled by the affect of the
other pulse.

Once the two pulses pass through each other,
there is still an upward displaced pulse and a
downward displaced pulse heading in the same
direction that they were heading before the
interference.
The two interfering waves do not need to have
equal amplitudes in opposite directions for
destructive interference to occur.
 For example, a pulse with a maximum
displacement of +1 unit could meet a pulse with a
maximum displacement of -2 units. The resulting
displacement of the medium during complete
overlap is -1 unit.


In this case, the destructive nature of the interference
does not lead to complete cancellation.

The meeting of two waves along a medium does
not alter the individual waves or even deviate
them from their path.


The task of determining the shape of the
resultant demands that the principle of
superposition is applied.
Principle of Superposition:

When two waves interfere, the resulting
displacement of the medium at any location is the
algebraic sum of the displacements of the
individual waves at that same location.
Displacement
of Pulse 1
Displacement
of Pulse 2
=
Resulting
Displacement
+1
+1
=
+2
-1
-1
=
-2
+1
-1
=
0
+1
-2
=
-1
EXAMPLES

1. Several positions along the medium are
labelled with a letter. Categorize each labelled
position along the medium as being a position
where either constructive or destructive
interference occurs.
Constructive Interference: G, J, M and N
 Destructive Interference: H, I, K, L, and O


2. Twin water bugs Jimminy and Johnny are
both creating a series of circular waves by
jiggling their legs in the water. The waves
undergo interference and create the pattern
represented in the diagram. The thick lines in
the diagram represent wave crests and the thin
lines represent wave troughs. Several of positions
in the water are labeled with a letter. Categorize
each labeled position as being a position where
either constructive or destructive interference
occurs
Constructive Interference: A and B
 Destructive Interference: C, D, E, and F
