• 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)

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

• 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 predict the relationships between systems or between components of a system. (9-12)

• Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)
  • Use a computational representation of phenomena or design solutions to describe and/or support claims and/or explanations. (9-12)

• 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: 9B/H1b. Sometimes the rate of change of something depends on how much there is of something else (as the rate of change of speed is proportional to the amount of force acting).
• 9-12: 9B/H5. When a relationship is represented in symbols, numbers can be substituted for all but one of the symbols and the possible value of the remaining symbol computed. Sometimes the relationship may be satisfied by one value, sometimes by more than one, and sometimes not at all.

• 6-8: 11B/M4. Simulations are often useful in modeling events and processes.
• 6-8: 11B/M5. The usefulness of a model depends on how closely its behavior matches key aspects of what is being modeled. The only way to determine the usefulness of a model is to compare its behavior to the behavior of the real-world object, event, or process being modeled.
• 9-12: 11B/H1a. A mathematical model uses rules and relationships to describe and predict objects and events in the real world.
• 9-12: 11B/H2. Computers have greatly improved the power and use of mathematical models by performing computations that are very long, very complicated, or repetitive. Therefore, computers can reveal the consequences of applying complex rules or of changing the rules. The graphic capabilities of computers make them useful in the design and simulated testing of devices and structures and in the simulation of complicated processes.

Mobile-ready resource lets you explore basic wave properties. View as a transverse or longitudinal wave and adjust the frequency, speed, and amplitude of the wave. Values of wavelength, period, and speed are automatically displayed. Editor's Note: This simulation would be an effective way to help learners see the distinction between particle motion and wave motion, an area of common misunderstanding.

• Conceptual Physics Modeling Wave Behavior Unit
• Algebra-Based Physics Modeling Wave Behavior Unit
• AP/Calculus-Based Physics Modeling Wave Behavior Unit