April 8 – April 9
Can two different objects occupy the exact same location at the
exact same time?
Of course not … but two waves can!
When waves meet, they superimpose (add together), but then
continue traveling unaltered, as if they had never had contact.
The superimposition of waves can create complex wave patterns.
Constructive interference
Occurs when both waves oscillate the
particles of medium in the same direction
at a given point in space.
Causes an increase in amplitude (and
thus energy) at that point.
Causes bright spots / loud sounds /
increase in vibration
Destructive interference
Occurs when the two waves oscillate the
particles of the medium in opposite
directions at a given point in space.
Causes a decrease in amplitude (and thus
energy) at that point.
Causes a decrease (or absence!) of light,
sound, vibration
Constructive interference occurs
when waves are in phase
Partially
destructive
interference
occurs when
waves are out
of phase by
any value
Completely destructive
interference occurs other
when than
waves
are 180 degrees out180.
of phase
When two waves interfere, the resulting displacement of the medium
at any location is the sum of the displacements of the individual waves
at that same location
Blue
Position Displacement
Red
Displacement
Total
A
0
0
0
B
3
1
4
C
D
E
F
G
Example: To find the resulting wave pattern for the two interfering waves
shown above, simply add the displacements of each wave at each point.
When two waves interfere, the resulting displacement of the medium
at any location is the sum of the displacements of the individual waves
at that same location
Blue
Position Displacement
Red
Displacement
Total
(green)
A
0
0
0
B
3
1
4
C
4
2
6
D
3
1
4
E
0
0
0
F
-3
-1
-4
G
-4
-2
-6
Example: To find the resulting wave pattern for the two interfering waves
shown above, simply add the displacements of each wave at each point.
Is this an example of constructive or destructive interference? constructive
Draw the interference pattern for the two waves shown on the graph
below. (Do at least to point J)
Which points have
constructive
interference?
Which points have
destructive
interference?
Draw the interference pattern for the two waves shown on the graph
below. (Do at least to point J)
Which points have
constructive
interference?
G, J
Which points have
destructive
interference?
H, I
Two boys, each 10 m apart, are splashing, creating identical waves
of wavelength 2 m that travel towards each other. Their little sister
is playing in between them, located 4 m away from one boy, 6 from
the other.
Will the waves by the sister
be big (due to constructive
interference) or small (due
to destructive
interference)?
How can we tell?
We have to determine whether the waves are in phase at point of the sister, or
not. To do this, we can compare the path length of the two waves. If the
difference in path length equals a whole wavelength (or a multiple 2λ, 3λ, 4λ,
etc.) then the waves will be in phase.
Two boys, each 10 m apart, are splashing, creating identical waves
of wavelength 2 m that travel towards each other. Their little sister
is playing in between them, located 4 m away from one boy, 6 from
the other.
Will the waves by the sister
be big (due to constructive
interference) or small (due
to destructive
interference)?
Path for wave from left = 4 m
Path for wave from right = 6 m
Difference = 6 m – 4 m = 2m
2 m = 1 whole wavelength
The two waves will add together
constructively, resulting in large waves
where the sister is swimming.
X and Y are coherent sources of 2cm waves.
At each of the following points, determine
whether they interfere constructively or
destructively.
A-
Destructive.
Path difference is
1cm which is ½ λ
B-
Constructive.
Path difference is
zero.
C-
Constructive.
Path difference is
two, which is 1λ
The wavelength of a transverse wave is 4cm. At
some point on the wave the displacement is -4cm.
At the same instant, at another point 50cm away
in the direction of propagation of the wave, the
displacement is
A. 0cm
We have to find out what
phase of the wave is 50 cm
B. 2cm
away.
C. 4cm
50 cm/ 4cm = 12.5
The other point is half a
D. -4cm
o
wavelength off / 180 out
of phase.
Reflected path
Direct path
Homes near cliffs
often have
interference
between direct
and reflected
signals
Momentary
interference
due to passing
airplane!
Noise-canceling headphones create sound
waves 180o out of phase with ambient noise
to cancel out the sound
Instruments are tuned with a tuning fork by
listening for beats – fluctuation in the
loudness of the sound – when both the
instrument and the tuning fork are played
together. If the instrument is out of tune, then
the wavelengths of the two notes will not
match and will fluctuate between constructive
and destructive interference, creating the
beats. The beats disappear when the
instrument is in tune.