This tutorial provides explanations and models of wave superposition. It includes multiple animations showing what happens when two waves move through the same region of space at the same time. Included are models of single and double-source interference, simulated oscilloscopes showing sine waves combining, and explanations of path and phase difference. Also included is a detailed explanation of the origin of pi and radians, plus a simple experiment that explores two sound sources interfering. A self-test is provided at the end of the tutorial.

This item is part of a larger collection of multimedia tutorials on waves and acoustics, developed by the University of Salford, UK. The tutorials are accompanied by more than 60 high-speed videos and animations that represent fundamental properties of waves.

Please note that this resource requires
Shockwave, or at least version 6.0 of Flash.

9-12: 4F/H6ab. Waves can superpose on one another, bend around corners, reflect off surfaces, be absorbed by materials they enter, and change direction when entering a new material. All these effects vary with wavelength.

11. Common Themes

11B. Models

6-8: 11B/M4. Simulations are often useful in modeling events and processes.

9-12: 11B/H1a. A mathematical model uses rules and relationships to describe and predict objects and events in the real world.

Common Core State Standards for Mathematics Alignments

High School — Algebra (9-12)

Creating Equations^{?} (9-12)

A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

A-CED.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Reasoning with Equations and Inequalities (9-12)

A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

High School — Functions (9-12)

Interpreting Functions (9-12)

F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.^{?}

Trigonometric Functions (9-12)

F-TF.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

F-TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

F-TF.4 (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

F-TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.^{?}

Common Core State Reading Standards for Literacy in Science and Technical Subjects 6—12

Craft and Structure (6-12)

RST.11-12.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 11—12 texts and topics.

Range of Reading and Level of Text Complexity (6-12)

RST.11-12.10 By the end of grade 12, read and comprehend science/technical texts in the grades 11—CCR text complexity band independently and proficiently.

<a href="https://www.compadre.org/portal/items/detail.cfm?ID=8744">University of Salford. University of Salford Tutorials: Superposition of Waves. Greater Manchester: University of Salford, January 1, 2019.</a>

University of Salford Tutorials: Superposition of Waves (University of Salford, Greater Manchester, 2005), <http://salfordacoustics.co.uk/sound-waves/superposition>.

University of Salford Tutorials: Superposition of Waves. (2019, January 1). Retrieved June 7, 2023, from University of Salford: http://salfordacoustics.co.uk/sound-waves/superposition

University of Salford. University of Salford Tutorials: Superposition of Waves. Greater Manchester: University of Salford, January 1, 2019. http://salfordacoustics.co.uk/sound-waves/superposition (accessed 7 June 2023).

University of Salford Tutorials: Superposition of Waves. Greater Manchester: University of Salford, 2005. 1 Jan. 2019. 7 June 2023 <http://salfordacoustics.co.uk/sound-waves/superposition>.

@misc{
Title = {University of Salford Tutorials: Superposition of Waves},
Publisher = {University of Salford},
Volume = {2023},
Number = {7 June 2023},
Month = {January 1, 2019},
Year = {2005}
}

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