Objectives
Describe constructive and destructive interference
of waves
Determine the resultant of two or more waves,
using the Principle of Superposition
Describe the shape and properties of a standing
wave
Determine the wavelength of interfering waves
using a standing wave diagram
Relate frequency to wave speed and the
dimensions of a standing wave pattern
Wave Interference
Waves rarely occur just by themselves. Usually we
have many waves occurring.
Wave Interference
What do you think happens when two waves meet
one another?
They bounce off each other and reflect?
They die immediately?
They pass through one another?
Something else?
** The waves pass through one another, but create
interference
Wave Interference
Interference doesn’t affect the
individual waves
Interference only affects the
individual particles of the medium
Interference only affects amplitude
Constructive Interference
2 waves with positive amplitude move towards one
another, or
2 waves with negative amplitude move towards one
another
Resulting wave amplitude will be larger than
original wave amplitudes
Wave
Interference
Constructive Interference:
p. 323
Wave Interference
Destructive Interference:
2 waves, one with positive amplitude, one with
negative amplitude move towards one another
Resulting wave amplitude will be smaller than
original wave amplitudes
Wave Interference
Destructive Interference:
p. 324
Principle of Superposition
Wave amplitude = displacement of its individual
particles from rest position
A transverse wave crest is made up of positive
particle displacements
A transverse wave trough is made up of negative
particle displacements
Principle of Superposition
+
=
Particle displacement of wave 1
Particle displacement of wave 2
Resultant particle displacement
Principle of
Superposition
a
b
Constructive Interference
(Wave amplitude)P =
(Wave amplitude)A + (Wave
amplitude)B
a
P=a+b
b
b
a
Principle of
Superposition
Destructive
Interference
a
c
(Wave amplitude)P =
(Wave amplitude)A (Wave amplitude)C
a
P=a-c
c
Standing
Waves
Skookumchuk
Narrows
Standing Waves
A special case of wave interference
2 waves (same wavelength/amplitude) traveling in
opposite directions, creates a standing wave
Standing Waves
When 2 like waves meet
(Same A & λ), There is a
point that never moves.
This point is called a Node
Standing wave in a vibrating string
Create a standing wave…
Standing Wave
Where do like waves (same A & λ) commonly
meet?
Standing waves are commonly found when a wave
meets its reflection (Echo)
Incident (A & λ) = Reflected (A & λ) but are
headed in opposite directions
Standing Waves
Loops
Nodes
Practice Questions
Heath p. 327 - #1 & #2
Summary
Waves passing through one another do not affect
each other, only the medium is affected
Principle of Superposition is the sum of the
individual wave displacements
Constructive interference: resultant waveform is
larger than the individual waves
Destructive interference: resultant waveform is
smaller than the individual waves
Nodes are continuously at rest
Loops are always have constructive interference
A pattern of nodes & loops = standing wave
Distance between nodes = ½ wavelength
Homework
Heath p. 342 #33, 35, 38, 39, 41, 42
Plus handout.