Energy balance in noise cancelling headphones

[stereoguy]

TL;DR Summary

Where does the energy go in active noise cancelling headphones?

Hi all,

You know active noise cancelling headphones. They create silence by emitting sound that is in the opposite phase compared to the incoming noise. (And perhaps similar systems could be used in larger spaces as well?)

Sound waves transport energy. What happens to this energy in active noise cancelling headphones?

I googled a bit and there seem to be two different answers:

1) Constructive and destructive interference - the silence is local, and there will be slightly more noise somewhere else. Energy stays in the sound waves (and some more sound energy is released by the ANC system).

2) The energy that enters the noise cancelling area is dissipated in the noise cancelling circuitry as heat.
(A clever engineer might try to build a power electronic converter that harvests a part of this energy for some useful purpose?)


Which answer is true, or if both are, which is more significant in practical applications?


To me, answer 1) sounds natural, it follows the fundamentals of waves. But I see something reasonable in answer 2) as well.

 

[sophiecentaur]

TL;DR Summary: Where does the energy go in active noise cancelling headphones?

The energy that enters the noise cancelling area is dissipated in the noise cancelling circuitry as heat.

Afaics, the two suggestions are actually equivalent - if you are trying to do the absorption actively; you have to drive a surface to match the vibrations of the arriving sound in some way. This is, in effect, using interference. In most places and directions, you won't get a cancellation. There are, of course, materials which dissipate certain sound frequencies (felt / foam / egg boxes) and you can achieve pretty good 'silence' in an anechoic chamber but they tend to be several cubic metres and are full of sponge wedges with a listening volume of just a couple of metres cube. Not ideal for home builty quietness.

PS Do forget the idea of Energy Harvesting for small sound levels. Jet engines sometimes can be a source of 'free energy' but most systems for free energy actually pinch energy from passing taffic or pedestrians so someone else pays!!

 

[stereoguy]

Afaics, the two suggestions are actually equivalent - if you are trying to do the absorption actively; you have to drive a surface to match the vibrations of the arriving sound in some way. This is, in effect, using interference. In most places and directions, you won't get a cancellation. There are, of course, materials which dissipate certain sound frequencies (felt / foam / egg boxes) and you can achieve pretty good 'silence' in an anechoic chamber but they tend to be several cubic metres and are full of sponge wedges with a listening volume of just a couple of metres cube. Not ideal for home builty quietness.

PS Do forget the idea of Energy Harvesting for small sound levels. Jet engines sometimes can be a source of 'free energy' but most systems for free energy actually pinch energy from passing taffic or pedestrians so someone else pays!!

Hm, hm, all this sounds reasonable.

But if we think about the world around the noise cancelling headphones, will there be more or less sound energy in total when noise cancelling is active? Some energy is dissipated as heat, but does the headphone output sound waves (energy) to some other directions?

Do we have a lower limit for the electrical energy that must be supplied to the noise cancelling circuitry? Does it approach zero if we have an extremely sensitive speaker for counter-noise generation?


edit:
Not sure if my edits are pending approval or not, but let's put an example here:

Let's say there's a sound source that is emitting 100 watts of noise power to all directions. There's a person standing near the source. 1 mW of noise power enters the ears of this person. The person starts using noise cancelling headphones and now 0 watts of noise enter the person's ears.

But what if we measure sound power over a sphere that encloses both the source and the person - how much sound power is now flowing out of the sphere?

 

[Bill Simpson]

If it is too difficult to solve the actual problem then see if anything can be learned from seeing if you can solve a simpler problem. Suppose all the sound is contained in cylindrical tube. One end of the tube is the noise generating speaker and the other end of the tube is the noise cancelling speaker. My first guess is that both speakers must produce exactly the same amount of power with a phase shift needed to exactly build a standing wave between them. So "behind" the cancelling speaker the two sounds need to sum to zero. That seems clear. What happens between the two speakers and what happens "behind" the generating speaker? Is this over-simplified model simple enough to let you produce a really convincing solution? From that can you find a slightly less over-simplified model that is still simple enough to produce a really convincing solution? From that can you give a convincing description of the original problem?

 

[sophiecentaur]

does the headphone output sound waves (energy) to some other directions?

Yes but the level will be much lower than ambient if the phones have some screening. The electronics would just clear up whagt gets through the absorber.

My first guess is that both speakers must produce exactly the same amount of power with a phase shift needed to exactly build a standing wave between them

If you are relying on a standing wave to help you then it will only null when the path lengths are exactly half wave different. For 'perfect' cancellation, the region that it works for will always be small so that the phases are more or less the same for cancellation

 

[Rive]

You know active noise cancelling headphones. They create silence by emitting sound that is in the opposite phase compared to the incoming noise. (And perhaps similar systems could be used in larger spaces as well?)

You have to be mindful of the available space (between the membrane of the headphone and your eardrum).
Compared to the wavelengths in question it's small, there is not much space for real, 3D interference: almost strictly linear, localized issue.
Also, the insulation around this area is relatively good.

In any larger space it's a 3D, multi-frequency issue with poor or nonexistent insulation => there are some means, but only with low effectiveness.

Let's say there's a sound source that is emitting 100 watts of noise power to all directions. There's a person standing near the source. 1 mW of noise power enters the ears of this person. The person starts using noise cancelling headphones and now 0 watts of noise enter the person's ears.

You have that earphone raising the noise level of the environment by some >1mW as an emitter.

When you have the incoming part cancelled by inverted (180 degree) shift and amplification, you also have it emitted on the other side.

 

[stereoguy]

You have that earphone raising the noise level of the environment by some >1mW as an emitter.

When you have the incoming part cancelled by inverted (180 degree) shift and amplification, you also have it emitted on the other side.

So, this would mean that the answer option nr. 2 in my original post (dissipating noise power as heat) is wrong. And using active noise cancellation in some local target actually increases the amount of noise in the surrounding environment. And active absorption with just speakers is not possible?

That is correct?

Yeah I can see that larger spaces are a different story. My main point was the question of where the energy goes.

 

[sophiecentaur]

And active absorption with just speakers is not possible?

A good question and there are similar systems for holding an object stationary in the presence of incoming vibrations. Feedback of the sound pressure at the surface of the speaker can be used to keep the surface stationary. That would involve absorbing the incident sound energy . So I don't think there's anything fundamentally wrong about the idea. But the ear is not at the surface of the speaker so there would be sound elsewhere, I think. And the body of the equipment would have to follow conservation of momentum.
I do wonder about the degree of attenuation and even the stability of such a system.