**Title:** Do You Hear What I Hear?

**Description:**
In this lesson, from Illuminations, students explore the dynamics of a sound wave. Students use an interactive Java applet to view the effects of changing the initial string displacement and the initial tension.

**Standard(s): **

[S1] (8) 12: Classify waves as mechanical or electromagnetic.

[S1] PHS (9-12) 9: Compare methods of energy transfer by mechanical and electromagnetic waves.

[S1] PHY (9-12) 6: Describe wave behavior in terms of reflection, refraction, diffraction, constructive and destructive wave interference, and the Doppler effect.

[MA2013] AL1 (9-12) 28: 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. *Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.** [F-IF4]

[MA2013] AL1 (9-12) 45: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [S-ID6]

[MA2013] AL2 (9-12) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [F-IF5]

[MA2013] AL2 (9-12) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [F-IF7]

[MA2013] AL2 (9-12) 34: 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-BF3]

[MA2013] PRE (9-12) 16: 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. (*Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Determine odd, even, neither.*)* [F-IF4] (Alabama)

[MA2013] ALT (9-12) 29: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.* [F-IF5]

[MA2013] ALT (9-12) 30: Graph functions expressed symbolically, and show key features of the graph, by hand in simple cases and using technology for more complicated cases.* [F-IF7]

[MA2013] ALT (9-12) 31: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. [F-IF8]

[MA2013] ALT (9-12) 32: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [F-IF9]

[MA2013] ALT (9-12) 33: Write a function that describes a relationship between two quantities.* [F-BF1]

[MA2013] ALT (9-12) 34: 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-BF3]

[MA2013] ALT (9-12) 40: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.* [F-TF5]

[MA2013] PRE (9-12) 26: Determine the amplitude, period, phase shift, domain, and range of trigonometric functions and their inverses. (Alabama)