Siren Song
Does the same sound always sound the same?
Students will
- Explore the relationship between frequency, wavelength, and pitch of a sound
- Write an equation for wavelength in terms of frequency for the sound emitted by a stationary object
- Describe how the frequency of sound emitted by a moving object will appear different to stationary observers in front of and behind the object two observers
- Write a formula for the observed wavelength of a sound wave in terms of the wave’s actual frequency and the speed of the object emitting the sound
- Write a formula for the observed frequency of a sound wave in terms of the wave’s actual frequency and the speed of the object emitting the sound
- Describe how observers will experience sound emitted from an object as it moves past the speed of sound
Before you begin
Students should be relatively comfortable working with variables in expressions and equations, and should be able to solve for one variable in terms of another.Common Core Standards
Content Standards
Mathematical Practices
Downloads
Shoutouts
Christian Doppler
Related Lessons
Sharper Image
Should you buy a camera lens with vibration reduction? Students interpret graphs and use right triangle trigonometry to explore the relationship between focal length, viewing angle, and blurriness.
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.
You're So Fined
How do municipal fines affect people with different incomes? Students write, solve, and graph systems of linear equations to determine how long it takes to pay off a ticket and debate the fairest ways for cities to raise revenues without harming their poorest residents.
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.
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.
Wage War
Should the government increase the minimum wage? Students use systems of linear equations to explore the relationship between wage and labor, analyze the economics of fast-food restaurants, and debate whether the federal government should increase the minimum wage.
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.
Datelines
How much does age matter in a relationship? Students use a system of linear inequalities to explore the popular dating rule-of-thumb, ‘half plus seven’, and debate how important age -- and other factors -- are in healthy relationships.
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.
