Active Noise Cancelling
Functions & Equations
How active noise-cancelling headphones work, and why they can't cancel everything.
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
Active noise-cancelling headphones listen to the incoming sound and play back an inverted copy of it, timed so the two waves cancel at your eardrum. Model both waves as sine functions and add them: get the phase right and they cancel almost completely; get it slightly wrong and they don't. This is also why noise cancelling works far better on a low engine drone than on a crowd's chatter — wavelength matters. You can test this directly with two speakers and a phone microphone, mapping out where in a room two sound waves add up and where they cancel.
Guiding Questions
- Noise-cancelling headphones play back an inverted copy of the incoming sound. What does adding two sound waves together mean mathematically?
- Model a noise tone and its inverted copy as sine functions with the same frequency but opposite phase. What happens when you add them, and what happens if the phase is slightly off?
- Why does cancellation work better for low frequencies than high ones? Investigate using wavelength.
- Set up two speakers playing the same tone and use a phone's sound meter to map where in a room the waves cancel and where they reinforce.