• Use mathematical representations to describe a simple model for waves that includes how the amplitude of a wave is related to the energy in a wave. (MS-PS4-1)
• Develop and use a model to describe that waves are reflected, absorbed, or transmitted through various materials. (MS-PS4-2)

• Use mathematical representations to support a claim regarding relationships among the frequency, wavelength, and speed of waves traveling in various media. (HS-PS4-1)

• A simple wave has a repeating pattern with a specific wavelength, frequency, and amplitude. (6-8)
• The wavelength and frequency of a wave are related to one another by the speed of travel of the wave, which depends on the type of wave and the medium through which it is passing. (9-12)

• Patterns can be used to identify cause and effect relationships. (6-8)
• Graphs, charts, and images can be used to identify patterns in data. (6-8)

• Models can be used to represent systems and their interactions—such as inputs, processes and outputs—and energy and matter flows within systems. (6-8)
• Models can be used to predict the behavior of a system, but these predictions have limited precision and reliability due to the assumptions and approximations inherent in models. (9-12)

• Analyzing data in 6–8 builds on K–5 and progresses to extending quantitative analysis to investigations, distinguishing between correlation and causation, and basic statistical techniques of data and error analysis. (6-8)
  • Analyze and interpret data to provide evidence for phenomena. (6-8)
• Analyzing data in 9–12 builds on K–8 and progresses to introducing more detailed statistical analysis, the comparison of data sets for consistency, and the use of models to generate and analyze data. (9-12)
  • Analyze data using computational models in order to make valid and reliable scientific claims. (9-12)

• Modeling in 6–8 builds on K–5 and progresses to developing, using and revising models to describe, test, and predict more abstract phenomena and design systems. (6-8)
  • Develop a model to describe unobservable mechanisms. (6-8)
• Modeling in 9–12 builds on K–8 and progresses to using, synthesizing, and developing models to predict and show relationships among variables between systems and their components in the natural and designed worlds. (9-12)
  • Use a model to provide mechanistic accounts of phenomena. (9-12)

• 6-8: 4F/M4. Vibrations in materials set up wavelike disturbances that spread away from the source. Sound and earthquake waves are examples. These and other waves move at different speeds in different materials.
• 6-8: 4F/M7. Wave behavior can be described in terms of how fast the disturbance spreads, and in terms of the distance between successive peaks of the disturbance (the wavelength).
• 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.

• 6-8: 11B/M1. Models are often used to think about processes that happen too slowly, too quickly, or on too small a scale to observe directly. They are also used for processes that are too vast, too complex, or too dangerous to study.
• 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.

This PhET favorite has been converted to HTML5 -- all ready for mobile devices and tablets. As the sim opens, you can "wiggle" a string to set up a manual pulse or make waves. Or, choose "Oscillator" and traveling or standing waves will be auto-generated. Students can set amplitude, frequency, damping, and string tension, then observe the results. Finally, students can view the string's vibration with a fixed end, a loose end, or no end.  See related teacher-created activity (directly below), developed for use in middle school classrooms with "Wave On a String".

• Physical Sciences K-8 Wave Properties: Frequency, Amplitude, Period, Phase Unit
• Physics First Wave Properties: Frequency, Amplitude, Period, Phase Unit
• Conceptual Physics Wave Properties: Frequency, Amplitude, Period, Phase Unit
• Algebra-Based Physics Wave Properties: Frequency, Amplitude, Period, Phase Unit
• AP/Calculus-Based Physics Wave Properties: Frequency, Amplitude, Period, Phase Unit

This activity lets students explore the fundamentals of frequency, amplitude, and damping in a simple wave/string system.  Waves can be manually or automatically generated with tension settings from low to high. View the wave as a pulse or as a driven oscillation. Choose a fixed end, loose end, or no end. Values of amplitude and frequency can also be adjusted, giving a great opportunity for bringing in math.

• Physics First How Waves Move and Interact: Reflection, Refraction, Interference Unit
• Conceptual Physics How Waves Move and Interact: Reflection, Refraction, Interference Unit
• Algebra-Based Physics How Waves Move and Interact: Reflection, Refraction, Interference Unit
• AP/Calculus-Based Physics How Waves Move and Interact: Reflection, Refraction, Interference Unit