12.4 Wave interactions
1. Apply superposition principle
2. Differentiate between constructive and destructive
inference.
3. Predict when a reflect wave will be inverted.
4. Predict whether specific traveling waves will produce a
standing wave.
5. Identify nodes and antinodes of a standing wave.
Wave Interference
• A phenomenon which occurs when two WAVES MEET while
traveling along the same medium.
• The interference of waves causes the medium to take on a
shape which results from the SUPERPOSITION of the two
individual waves.
The two waves meet, produce a
net resulting shape of the
medium, and then CONTINUE on
doing what they were doing
before the interference.
Constructive interference
• Occurs where the two interfering waves have a displacement in
the same direction. The result is a LARGER AMPLITUDE.
MAXIMUM constructive
interference occurs when the
waves are in PHASE (phase
difference is 0o or 360o) and
crest superposes on crest or
trough on trough.
1 unit
2 units
The point of maximum displacement
of a medium when two waves are
interacting is called an ANTI-NODE.
-1 unit
-2 units
Destructive interference
• Occurs where the two interfering waves have a displacement in
the opposite direction. Destructive interferences result a
SMALLER amplitude.
• Maximum destructive interference occurs when two waves of
equal frequency and amplitude whose phase difference is 180o
or ½ λ meet at a point. Maximum destructive interference
results in the formation of NODES. Which are regions of ZERO
displacement of the medium
Constructive
Destructive
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
Example #1
Determine type of interference of each section as constructive or destructive.
III
I
II
Example #2
Apply superposition principle to determine result of interference by sketch the
resultant wave.
CLASS WORK – today’s date
1.
a.
b.
2.
Two waves having the same amplitude and the same
frequency pass simultaneously through a uniform
medium. Maximum destructive interference occurs when
the phase difference between the two waves is
0°
c. 90°
180°
d. 360°
The diagram shows two pulses, each of length, traveling toward each other at
equal speed in a rope. Which diagram below best represents the shape of the
rope when both pulses are in region AB?
a.
b.
c.
d.
3.
Maximum constructive interference between two waves of
the same frequency could occur when their phase difference
is
a. 1λ
b. ¼ λ
c. ½ λ
d. 1 ½ λ
4.
The diagram below represents shallow water waves of wavelength λ passing through
two small openings, A and B, in a barrier. How much longer is the length of path AP
than the length of path BP?
a. 1λ b. 2λ
c. 3λ
d. 4λ
5. The diagram below represents shallow water waves of
constant wavelength passing through two small openings, A
and B, in a barrier. Compared to the length of path BP, the
length of path AP is how many wavelength longer?
6. Which statement best describes the interference at point P?
a. It is constructive, and causes a longer wavelength.
b. It is constructive, and causes an increase in amplitude.
c. It is destructive, and causes a shorter wavelength.
d. It is destructive, and causes a decrease in amplitude.
7.
The diagram shows two sources, A and B, vibrating in phase
in the same uniform medium and producing circular wave
fronts. Which phenomenon occurs at point P?
a. destructive interference
b. constructive interference
c. reflection
d. refraction
8. Determine the interference pattern
Reflection of a Pulse
Fixed Point
Floating Point
before
before
after
after
The reflected pulse is INVERTED. This
inversion can be explained by Newton's third
law of action-reaction.
The reflected pulse have the SAME
DIRECTION as the incident pulse.
Changing Mediums
Fast  Slow
Slow  Fast
less dense  denser
denser  less dense
before
before
after
after
Characteristics of transmitted pulse and
reflected pulse
• The wave speed is always GREATEST IN THE LEAST dense
rope.
• The wavelength is always GREATEST IN THE LEAST DENSE
rope.
• The frequency of a wave is NOT ALTERED by crossing a
boundary.
• The reflected pulse becomes INVERTED when a wave in a less
dense rope is heading towards a boundary with a denser
rope.
• The amplitude of the incident pulse is always greater than the
amplitude of the reflected pulse.
Example
•
A pulse moves from a very thick rope into a thin string. Circle
the term that makes the statement true.
a. The transmitted pulse will lose / gain amplitude.
b. The transmitted pulse will lose / gain speed.
c. The transmitted pulse will lose / gain energy.
d. The reflected pulse will / will not come back on the opposite
side.
Two sources in phase in the same medium
crests
troughs
Constructive: Point A, B are anti-nodes
Destructive: Point C, D, E, F are nodes
Standing Waves
• A WAVE PATTERN what results when two waves of the SAME
frequency, wavelength, and amplitude travel in OPPOSITE
DIRECTIONS and interfere
• A standing wave pattern is formed as the result of the perfectly
timed interference of two waves passing through the same medium.
A standing wave is NOT actually A WAVE; rather it is the
PATTERN.
Nodes and anti-nodes in a standing wave
Nodes: the points of ZERO displacement of the resultant wave
Antinotes: the points of MAXIMUM displacement of a medium
The distance between two successive nodes is ½ λ
standingWaveDiagrams1/StandingWaveDiagrams1.html
1st harmonic
• Standing wave patterns are
only created within the
medium at SPECIFIC
FREQUENCIES OF
VIBRATION. These
frequencies are known as
HARMONICS.
• ..\..\RealPlayer
Downloads\Standing Wave on
a String.flv
• Standing waves can be
created for both transverse
and longitudinal waves.
• pipe-waves.html
2nd harmonic
3rd harmonic
Harmonic
# of
Nodes
# of Antinodes
1st
2
1
Pattern
λ
2L
2nd
L
3rd
2/3 L
4th
½L
5th
2/5 L
6th
1/3 L
nth
n+1
n
--
Standing waves in water
• Standing waves in water are produced most
often by periodic water waves REFLECTING
FROM A BARRIER.
Example #1
•
What is the number of nodes and antinodes
in the standing wave shown in the
diagram?
8 nodes
7 antinodes
Example #2
The diagram represents a wave moving toward the
right.
Which wave shown below could produce a standing
wave with the original wave?
1
2
3
4
Example #3
•
1.
2.
3.
4.
Two waves traveling in the same medium and
having the same wavelength (λ) interfere to create
a standing wave. What is the distance between two
consecutive nodes on this standing wave?
λ
½λ
¼λ
¾λ
Class work – today’s date
1. Sketch a pulse that shows the superposition of the
pulse pairs below.
2. A pulse with a height of +0.5 meter encounters a second
pulse with a height of +2.3 meters.
a. The two pulses interfere: ___________________________
b. The resulting height of the medium when the pulses interfere
will be: ______________ m
3. A pulse with an amplitude of 0.4 meter moves from a
thick, heavy cord where its speed is 2.0 meters per second
into a much thinner string. The speed and height of the
pulse after it is transmitted could be:
a.
b.
c.
d.
Amplitude = 0.5 m; Speed = 1.0 m/s
Amplitude = 0.3 m; Speed = 1.0 m/s
Amplitude = 0.5 m; Speed = 3.0 m/s
Amplitude = 0.3 m; Speed = 3.0 m/s
4.
Which of the following is transmitted by a pulse?
(1) energy and mass (2) mass only
(3) energy only
5.
The energy contained in a pulse is related to its:
(1) amplitude and speed
(3) width and speed
(2) amplitude only
(4) speed only
6.
As pulses travel they lose:
(1) amplitude and speed
(3) width and speed
(2) amplitude only
(4) speed only
7.
A pulse moves from a very thick rope into a thin string. Circle the term that
makes the statement true.
(a) The transmitted pulse will lose / gain amplitude.
(b) The transmitted pulse will lose / gain speed.
(c) The transmitted pulse will lose / gain energy.
(d) The reflected pulse will / will not come back on the opposite side.
8. Sketch the superposition of the following sets
of pulses.
9. The grid below represents a 10.0 meter long string.
a. Sketch the standing wave that this string would produce if it
were to have SIX nodes.
b. Draw a circle around each ANTINODE on the string.
c. Determine the wavelength of this standing wave.
_________________m
d. Assuming that this wave moves at 2.0 meters per second,
calculate its frequency and period.
10. Two point sources produce a pattern of overlapping circular
waves. The solid lines in the diagram represent wave crests
while the dotted lines represent wave troughs. Mark a “C” in
the boxes that indicate constructive interference and a “D” in
the boxes that indicate destructive interference.
11. Sketch a wave that will completely destructively interfere
with the wave shown below. What is the phase difference
between these two waves?
12. At the point when the two waves shown below completely
overlap, what will the superposition of the two waves look
like? Draw a sketch of the wave produced during this
interaction.
13. A standing wave is produced as a result of a combination of
_______________ and _______________________.
The main features of standing waves are:
______________________ at which minimum motion of the
medium occurs.
_______________________ at which maximum motion of
the medium occurs.
14. Determine the wavelength of the standing wave shown
below. Identify one node and one anti-node.
15. A (NODE/ANTINODE) is the result of an alternating phase
difference of 0 and 180 degrees between two waves passing
through each other. (Circle one)
16.To produce a standing wave, two waves must:
o be moving in _______________________________
o have the same:
_____________________________
_____________________________
_____________________________
17. The grid below represents a 10 meter long string.
–
–
–
–
Sketch the standing wave that this string would produce if it
were to have SIX nodes.
Draw a circle around each ANTINODE on the string.
Determine the wavelength of this standing wave.
_________________m
Assuming that this wave moves at 2.0 meters per second,
calculate its frequency and period.