Section 1: The Principle of Superposition & Interference
Define the Principle of Superposition of Waves.
When two or more waves of the same type meet at a point, the resultant displacement is the sum of the displacements of the individual waves.
What is the rule for adding displacements when waves meet?
Displacement is a vector, so individual displacements must be added while taking their directions into account.
What terms are used to describe the “adding-together” of waves?
Interference, superposition, or the overlap of waves.
List the two essential conditions for waves to interfere.
1) The waves must meet at a point. 2) The waves must be of the same type (e.g., both sound or both electromagnetic).
Define Coherence.
Coherence is when two waves have a fixed (constant) phase difference and the same frequency.
What is constructive interference?
It occurs when waves are in phase, resulting in a resultant amplitude greater than that of the individual interfering waves.
What is destructive interference?
It occurs when waves are out of phase (anti-phase), resulting in a resultant amplitude of zero.
What path difference is required for constructive interference if sources are in phase?
A path difference that is a whole number of wavelengths (nλ), where n = 0, 1, 2, 3…..
What path difference is required for destructive interference if sources are in phase?
A path difference that is a whole number of wavelengths plus a half wavelength: (n + 1/2)λ.
What are the phase difference values for constructive interference?
0, 2π, 4π, 6π, ….
What are the phase difference values for destructive interference?
π, 3π, 5π, 7π, ….
How do the path difference conditions change if the two sources have an initial 180^° phase difference?
The conditions swap: Constructive interference (maxima) occurs at (n + 1/2)λ and destructive interference (minima) occurs at nλ.
Section 2: Stationary (Standing) Waves
Define a stationary (standing) wave.
It is the superposition of two progressive waves of the same type, wavelength, and frequency, travelling in opposite directions at the same speed.
How is a stationary wave typically formed in a laboratory?
By a progressive wave moving in one direction and its own reflection moving in the opposite direction.
Why is it called a “stationary” wave?
Because energy is not travelling through the medium and the wave shape does not change.
Define a Node (N).
A point on a stationary wave that remains permanently at rest with zero oscillation/amplitude.
Define an Antinode (A).
A point on a stationary wave that has the maximum amplitude of oscillation.
What is the distance between two successive nodes or two successive antinodes?
One half of a wavelength (1/2λ).
What is the distance between a node and the next adjacent antinode?
One quarter of a wavelength (1/4λ).
How is wavelength defined in terms of nodes/antinodes?
It is double the separation between two adjacent nodes or two adjacent antinodes.
Describe the phase difference between two points on the same segment of a stationary wave.
The phase difference is 0^° (they are in phase).
Describe the phase difference between two points on adjacent (consecutive) segments of a stationary wave.
The phase difference is 180^° (they are in anti-phase).
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Estimates #130
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Chapter 1 #332
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Chapter 2 #218
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Chapter 3 #133
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Chapter 4 #233
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Chapter 5 #261
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Chapter 6 #250
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Chapter 7 #242
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Chapter 8 #492
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Chapter 9 #143
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Chapter 10 #248
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Physical Quantities and Measurement Techniques Definitions #134
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Mechanics Definitions #1121
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Waves and Superposition Definitions #153
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Electricity Definitions #135
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Nuclear Physics and Fundamental Particles Definitions #134
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All Formulae #1180
