• 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.

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

• 6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.

• A-SSE.2 Use the structure of an expression to identify ways to rewrite it.

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

• F-BF.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context.
• F-BF.1.c (+) Compose functions.
• F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

• F-TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.^?
• F-TF.7 (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.^?

This high-quality lesson plan was created to be used with the PhET simulation "Wave on a String".  Students will apply the concepts introduced in the computer simulation to explore frequency, amplitude, and tension on an oscillating string. Editor's Note: this lesson gives students the chance to model the movement of energy on a string by applying properties of sinusoidal function. A great integration of trigonometry and physics.....and it's fun!

• Algebra-Based Physics Simple Harmonic Motion Unit
• AP/Calculus-Based Physics Simple Harmonic Motion Unit

This is a computer lab created specifically for use with the PhET simulation "Wave on a String" (see Activities below).  Students apply trigonometry and analyze how frequency, amplitude, and tension influence the motion of the wave. NOTE: This resource is available only to registered PhET users, but registration is free, easy, and well worth your time.

• 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