The Sound of Silence
How do noise-canceling headphones work?
Students will
- Given the frequency of a pure tone, calculate the period of its sound wave
- Sketch the graph of a chord composed of two tones and estimate its period and frequency
- Describe any apparent relationship between a chord’s period and its perceived pleasantness
- Sketch the graph of a pure tone’s noise-canceling counterpart and construct multiple functions to describe it
- Develop general procedures for generating a noise-cancelling wave from a given pure tone
- Examine some difficulties in describing noise-canceling waves for chords
- Explain how noise-canceling headphones work and why they are not always completely effective
Before you begin
Students should be familiar with the general form of sinusoids (i.e. f(x) = Asin(Bx – C) + D or f(x) = Acos(Bx – C) + D) and how changes in the parameters affect their graphs.Common Core Standards
Content Standards
Mathematical Practices
Downloads
Additional Materials
- Graphing Technology
Shoutouts
Kyle Jones, Smithsonian; image courtesy of Patrik Theander (https://www.flickr.com/
photos/fabolous/8627113727/)
Related Lessons
Carpe Donut
How much should people pay for donuts? Students use linear, rational, and piecewise functions to describe the total and average costs of an order at Carpe Donut.
Sofa Away From Me
How far away from the TV should you sit? Students use right triangle trigonometry and a rational function to explore the percent of your visual field that is occupied by the area of a television.
Pyramid of Sleaza
How can you make money in a pyramid scheme? Students learn about how pyramid schemes work (and how they fail), and use geometric sequences to model the exponential growth of a pyramid scheme over time.
Loan Ranger
How much do you really pay when you use a credit card? Students develop an exponential growth model to determine how much an item really ends up costing when purchased on credit.
Fall of Javert
Could Inspector Javert have survived the fall? Students use quadratic models to determine how high the bridge was in Les Misérables, and explore the maximum height from which someone can safely jump.
XBOX Xponential
How have video game consoles changed over time? Students create exponential models to predict the speed of video game processors over time, compare their predictions to observed speeds, and consider the consequences as digital simulations become increasingly lifelike.
It's a Date
How can we improve our calendar? Students examine some other ways to keep track of dates, and use number sense and function concepts to convert between different calendars.
Driving Question
When should NFL teams go for it on fourth down? Students use quadratic functions to develop a model of expected points. They then apply this model to determine when teams should punt the ball, and more importantly, when they shouldn’t.
Wiibates
How much should Nintendo charge for a video game console? Students use linear and quadratic models to analyze and discuss the relationship between the price of a Wii U console and profits for Nintendo.
Pizza Pi (HS)
Which size pizza should you order? Students apply the area of a circle formula to write linear and quadratic formulas that measure how much of a pizza is actually pizza, and how much is crust.
Prescripted
How should pharmaceutical companies decide which drugs to develop? Students create linear and quadratic functions to explore how much pharmaceutical companies profit from different drugs and consider ways to incentivize companies to prioritize medications that are valuable to society.
Billions & Billions
How has the human population changed over time? Students develop exponential models to analyze human population growth and explore the impact this growth will have in areas around the world.
Connected
Do social networks like Facebook make us more connected? Students create a quadratic function to model the number of possible connections as a network grows, and consider the consequences of relying on Facebook for news and information.
House of Pain
Why are so many Americans dying from opiate overdoses? Students use exponential decay and rational functions to understand why addicted patients seek more and stronger opioids to alleviate their pain. Students discuss the role that various parties played in creating the crisis and ways they can help to solve it.
Mercury Rising
How have temperatures changed around the world? Students use periodic functions to compare long-term average monthly temperatures to recorded monthly temperatures, evaluate evidence of climate change, and discuss possible consequences.
Going Once, Going Twice
How much should you bid in an auction? Students create polynomial functions to model the expected value of a given bid and determine the optimal amount someone should bid in any auction.
Rise and Shine
What time should school start in the morning? Students use periodic functions to compare the alertness levels of adults vs. teenagers over the course of the day and debate the merits of starting school later.
Opportunities' Cost
Is higher education a good investment? Students write and solve systems of linear equations to determine how long it would take to pay off various degrees and discuss the pros and cons of different educational paths.
Second Degree
How dangerous are heat and humidity? Students use polynomial functions to explore the heat index and discuss the life-and-death consequences that cities around the world will face in the coming years.
Pandemic
How do viruses spread through a population? Students use exponential growth and logarithms to model how a virus spreads through a population and evaluate how various factors influence the speed and scope of an outbreak.
I Remember
How much should you trust your memory? Students use exponential decay to model memory fidelity and debate whether a bad memory is a good thing.
Canalysis
What’s the ideal size of a soda can? Students create rational functions to explore the relationship between volume, surface area, and cost to determine the optimal size of a soda can.
