| Lab Name |
Math behind the noise - cancellation headphones
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| Subject Area |
Math and Science
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| Grade |
8 - 12
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| Topic |
Evaluating and graphing piecewise functions
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| Experiment Title |
Destructive Interference
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| Hardware |
- COSMOS Toolkit: Computer Node
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| Software |
- COSMOS Toolkit: Framework
- GNU Radio
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| Number of Sessions to teach the topic |
2 - 3
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| Educational standards to be addressed |
- CCSS.Math.Content.HSF.TF.B.6
Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
- CCSS.Math.Content.HSF.TF.B.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.
- CCSS.Math.Content.HSA.REI.D.11
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
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| COSMOS concepts to be used for the lab |
Destructive Interference
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| K12 Educational Goals (How the educational goals are achieved through teaching using the experiment, how the topic is connected to the COSMOS concepts used) |
The students are able to graph piecewise functions with constraints. Students will evaluate piecewise and determine the resultant by adding the min and the max of two functions. Students are making the connection between the value of the resultant and how that value is affecting the performance of the noise- cancelling headphones, which is the concept of the destructive Interference.
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| Short Description and Walk-through of the experiment |
- Students will evaluate and graph piecewise functions. Then they will graph the same function reflected over the x-axis. Then students will determine the min and the max and combine the two values to get the resultant of zero which demonstrates the concept of destructive interference.
- The worksheets of this lesson consists of 4 parts. The activities are scaffolded such that it can be done by Algebra 1 and Algebra 2 students. It is up to the Instructor to do 1 or all 3 parts and the activity can be concluded by doing part 4.
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