Noise-canceling headphones can reduce a lot of ambient sound, but they are not 100% perfect. (Especially in the human vocal range.)

  1. Is there any physical principle preventing the creation of perfect sound-canceling headphones? In other words, headphones that can cancel or block 100% of all external sound before it reaches my ears. (I realize that I would still hear internal body sounds, of course.)

  2. Now, instead of headphones, how about a device that can cancel all the sound in the room for all the listeners in the room?

  • $\begingroup$ Wouldn't infinite loop gain be required to drive the error signal (residual external noise) to zero? $\endgroup$
    – Hal Hollis
    Jan 15 '19 at 16:05
  1. You can't get 100% cancellation. No analog quantity can be cancelled to infinite precision. However you don't need 100%, you only need to attenuate to the point where the residual noise drops below the threshold of hearing or gets masked by the noise floor.
  2. There are a lot of practical issues that makes this difficult (fit; electrical, material and mechanical tolerances; anthropomorphic variability, etc). A good noise cancelling headset attenuates the sound by about 30 dB (which is 1 millionth of the original energy). If your outside sound is 70 dBSPL and your threshold of hearing is 10dB SBL, you need to reduce the noise energy by another factor of one million to make it inaudible.
  3. There are other sound transmission paths that don't go through the outer ear. Primarily it's bone conduction through your body. In theory you could cancel these too with additional acoustic sound or a suitable mechanical actuator, but you would need to attach a sensor to your skull (preferably to the petrosal).
  4. Noise cancellation in a room is much harder and mostly impractical. The sound field is very complicated and the room tends to de-correlate sound. You would need lots and lots of independent drive points and also a large number of sensor. Even then, the results would be mediocre at best, unless the drive points and sensor are very close to the ear
  • $\begingroup$ "Noise cancellation in a room is much harder and mostly impractical" - I do want to mention a very specific counterexample. On turboprop aircraft much of the sound in the cabin is airflow off the prop tips hitting the fuselage and causing it to "buzz". Modern designs like the Q400 have piezo buzzers to counteract this motion ans cause whole-cabin noise cancellation. $\endgroup$ Jan 15 '19 at 19:43
  • $\begingroup$ 30 dB is hardly 1 millionth, did you mean 1 thousandth? $\endgroup$
    – pipe
    Feb 27 '19 at 12:39

Is there any physical principle preventing the creation of perfect sound-canceling headphones?

Yes. An active noise cancelling headphone contains a tiny microphone inside the ear cup, and the electronic circuit is pretty good at minimizing the sound level at the exact location of the microphone.

Your eardrum is not at the exact location of the microphone. It's pretty close though, and so the active noise cancellation works pretty well for frequencies whose wavelength are significantly larger than the distance separating your eardrum from the mic. But the higher the frequency (the shorter the wavelength), the less well the active noise cancellation works.

Fortunately, the effectiveness of sound absorbing materials (e.g., foam rubber) increases with frequency. Active noise cancelling headphones generally rely on the active electronics to minimize the low frequencies (the rumble of a jet engine), and they rely on the material properties of the ear cups to attenuate the higher frequencies (the crying baby in the seat behind you.)

Now, instead of headphones, how about a device that can cancel all the sound in the room for all the listeners in the room?

Nope: For the reason stated above, active noise cancellation only truly works at one exact point (the location of the microphone.) The further you get from that point, the less well it works. More than a few centimeters away, and it's not going to have any noticeable effect...

...Except, if the noise is a pure tone, emitted by a speaker in a fixed location, then that tone sets up standing waves in the room, and if you switch on an active noise canceller, it will emit a similar pure tone with a different standing wave pattern that will reduce the "noise" at many places in the room while reinforcing the "noise" at other places.

In a real situation, where the noise contains many frequencies, and it comes from many locations, then you'll be dealing with so many overlapping standing waves that you won't really be able to make any sense of it. On average, when you switch the machine on, you probably won't notice any change unless your ear is right next to the mic. That'll be the only location where all of the standing waves cancel each other out.

  • $\begingroup$ This is a wonderful answer and has deepened my understanding of sound. I only wish I could select more than one answer! $\endgroup$
    – SlowMagic
    Jan 16 '19 at 16:02

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