The Principle of Linear Superposition and Interference Phenomena 12/17/23, 11 : 59 PM
Chapter 17 The Principle of Linear
Superposition and Interference Phenome
Preview
When waves meet they combine in the region where they overlap to form a new wave. The new wave
disturbance is the sum of the disturbances of the original waves. This is called the Principle of Linear
Superposition. The result of the addition or superposition of the wave disturbances is called interferen
In this chapter you will learn how to superimpose waves and will study the resulting interference of two
generated by point sources or very narrow slits (interference patterns), many waves which have diffrac
through a single slit (diffraction patterns), two identical waves traveling in opposite directions (standin
and two waves of different frequencies (beats).
Quick Reference
17.1.1 Important Terms
Superposition The adding together of two or more wave disturbances to form a net disturbance.
Interference The result of the superposition of two or more waves.
Constructive The result of the superposition of two waves which meet exactly in phase. That is, crest
interference and trough to trough.
Destructive The result of the superposition of two waves which meet exactly out of phase. That is, c
interference trough and trough to crest.
Diffraction The bending of a wave around an obstacle or edges of an opening.
A periodic variation in the amplitude of a wave resulting from the linear superposition of
Beats
that have slightly different frequencies.
Standing The stationary pattern of disturbance produced when identical waves traveling in opposit
wave directions superimpose.
Node A point on a standing wave where the wave disturbance is zero.
Antinode A point on a standing wave where the wave disturbance is maximum.
Natural
The frequencies of waves necessary to produce resonance.
frequencies
A set of natural frequencies of a system which are related by being integer multiples of th
frequency, that is, , , , etc., where is the lowest frequency called the fundamen
Harmonics
first harmonic. The frequency is called the second harmonic, the frequency is ca
third harmonic, etc.
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, The Principle of Linear Superposition and Interference Phenomena 12/17/23, 11 : 59 PM
17.1.2 Equations
The position of the first minimum of a single slit diffraction pattern can be found from
(17.1)
The position of the first minimum of the diffraction pattern of a circular opening can be found from
(17.2)
The set of natural frequencies of a string fixed at both ends is given by
(17.3)
The set of natural frequencies of a tube open at both ends is given by
(17.4)
The set of natural frequencies of a tube open at only one end is given by
(17.5)
17.1.3 Principles
The Principle of Linear Superposition-when two or more waves are present simultaneously at the same
the resultant wave is the sum of the individual waves.
Discussion of Selected Sections
17.2 Constructive and Destructive Interference of Sound Waves
Any time that two or more waves overlap in space an interference pattern results. The pattern may be v
complicated if many waves of different amplitudes and frequencies overlap, or relatively simple if only
waves with the same amplitude and frequency are involved. Constructive interference occurs when the
are exactly in phase and destructive interference occurs when they are exactly out of phase.
Two waves originally in phase can get out of phase if they are required to travel different path lengths b
combining. If one wave travels , , , etc. farther than the other, then the two waves will be in phas
constructively interfere. If one travels , , , etc. farther than the other, then they will be ou
phase and will destructively interfere.
Example 1
Two in-phase speakers are located apart and produce identical tones. A person stands
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Chapter 17 The Principle of Linear
Superposition and Interference Phenome
Preview
When waves meet they combine in the region where they overlap to form a new wave. The new wave
disturbance is the sum of the disturbances of the original waves. This is called the Principle of Linear
Superposition. The result of the addition or superposition of the wave disturbances is called interferen
In this chapter you will learn how to superimpose waves and will study the resulting interference of two
generated by point sources or very narrow slits (interference patterns), many waves which have diffrac
through a single slit (diffraction patterns), two identical waves traveling in opposite directions (standin
and two waves of different frequencies (beats).
Quick Reference
17.1.1 Important Terms
Superposition The adding together of two or more wave disturbances to form a net disturbance.
Interference The result of the superposition of two or more waves.
Constructive The result of the superposition of two waves which meet exactly in phase. That is, crest
interference and trough to trough.
Destructive The result of the superposition of two waves which meet exactly out of phase. That is, c
interference trough and trough to crest.
Diffraction The bending of a wave around an obstacle or edges of an opening.
A periodic variation in the amplitude of a wave resulting from the linear superposition of
Beats
that have slightly different frequencies.
Standing The stationary pattern of disturbance produced when identical waves traveling in opposit
wave directions superimpose.
Node A point on a standing wave where the wave disturbance is zero.
Antinode A point on a standing wave where the wave disturbance is maximum.
Natural
The frequencies of waves necessary to produce resonance.
frequencies
A set of natural frequencies of a system which are related by being integer multiples of th
frequency, that is, , , , etc., where is the lowest frequency called the fundamen
Harmonics
first harmonic. The frequency is called the second harmonic, the frequency is ca
third harmonic, etc.
https://education.wiley.com/content/Cutnell_Physics_11e/media/simulations/ssg/c17/c17-body-0001_ref.html Page 1 of 11
, The Principle of Linear Superposition and Interference Phenomena 12/17/23, 11 : 59 PM
17.1.2 Equations
The position of the first minimum of a single slit diffraction pattern can be found from
(17.1)
The position of the first minimum of the diffraction pattern of a circular opening can be found from
(17.2)
The set of natural frequencies of a string fixed at both ends is given by
(17.3)
The set of natural frequencies of a tube open at both ends is given by
(17.4)
The set of natural frequencies of a tube open at only one end is given by
(17.5)
17.1.3 Principles
The Principle of Linear Superposition-when two or more waves are present simultaneously at the same
the resultant wave is the sum of the individual waves.
Discussion of Selected Sections
17.2 Constructive and Destructive Interference of Sound Waves
Any time that two or more waves overlap in space an interference pattern results. The pattern may be v
complicated if many waves of different amplitudes and frequencies overlap, or relatively simple if only
waves with the same amplitude and frequency are involved. Constructive interference occurs when the
are exactly in phase and destructive interference occurs when they are exactly out of phase.
Two waves originally in phase can get out of phase if they are required to travel different path lengths b
combining. If one wave travels , , , etc. farther than the other, then the two waves will be in phas
constructively interfere. If one travels , , , etc. farther than the other, then they will be ou
phase and will destructively interfere.
Example 1
Two in-phase speakers are located apart and produce identical tones. A person stands
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