Interference Inference

Last night I slept at my parents' new condo for the first time.  It's a nice place, but it's next to a couple busy streets, so there's a lot of car noise.  It got me thinking about active noise canceling, where a device picks up the background noise and replays it delayed by just the right amount that the two waves cancel.  Here's a quick example:

If the black curve is the original, the noise canceling device would produce the red curve.  Adding them together gives zero, no sound.

Things are a little more complicated in three dimensions, but it's still possible.  Let's say I want to cancel the noise from the street while I'm in bed.  I can put a speaker in a specific spot that replays the street noise shifted slightly.  The animation below shows the contours of the total of the two sound waves.  I'm at the blue dot.  Ideally, a silent spot would be a place that no contour lines cross, so I didn't get this tweaked perfectly, but you can see that the blue dot will be a lot quieter than other places.

 

One potential problem with this idea is the frequency of car noise.  It's around 1000 Hz, and a quick calculation shows it has a wavelength of about 13 inches.  That means that if you set things up to cancel at one ear, half a wavelength away at your other ear, the waves could add, making the noise twice as loud.  I might be better off with earplugs...