Which noises can noise cancelling headphones filter out? (Anders Jacobsen's blog)

January 11, 2007

Which noises can noise cancelling headphones filter out?

On the trend of me ploughing through emailed comments today, with the risk of making it a day of only headphone-postings, here is an interesting one from Alexandru Constantinescu, a Ph.D. at the Max-Planck-Institute of Molecular Cell Biology and Genetics, explaining why actively noisecancelling headphones couldn't filter out sirens etc even if they wanted (without some rather heavy computational power):

Hello there!

I was looking for an AAC vs MP3 comparison and found your blog entry (and some interesting comments below it). Then my attention got attracted by "How do noise canceling headphones work?" and after reading that, please allow me for a correction.

There's this myth that NC headphones "decide" to let sirens and voices go through, since you might want to hear them. This is a misconception. They simply could NOT cancel those things out.

As you say, there is this microphone in the headphones picking sounds from the ambient and applying a counter-wave, so that the noise cancels out. Now, let's do a bit of math: at 340m/s (sound speed in air), a 680Hz sound would have 2 full waves per meter, i.e. a wavelength of 0.5m. If the "noise" would come from your side, your left ear would sit on the top of a wave while your right ear would sit on the through of the same wave (assuming a rough 25cm between your ears). Thus, your NC electronics would have to play different waves in your right and left speakers (which might be manageable). However, there are two complications to this model:

1. if the sound comes from 1 o'clock, then the calculation would not hold anymore. You would need a directional microphone on each earcup to pick the direction of each noise.

2. everything here assumes there's 25cm between your ears, but we are actually interested in the distance between your eardrums (that's what you actually hear with) and also between your eardrums and the cups (since we have to factor in the time it takes the canceling wave to travel from the headphone speaker to your drum). And you can't properly factor those in.

So, there's a good physics reason why NC headphones let voices and sirens through and not the good will of the manufacturer.

On a different topic: very nice photo of the cabbie in NY.
Best regards and a Happy New Year!

Alexandru

Thanks for writing in, Alexandru, and thanks for highlighting these interesting facts!