This won't work. In addition to what others have said about different points in the room having different distances to the fan and speaker, there are other issues:
1. The fan's fundamental frequency isn't perfectly stable, so even if you are in a spot where there speaker's tone cancels with it, the fan will probably wander around that frequency enough that the cancellation won't work well.
2. The fan isn't just a fundamental tone + noise. There are also a whole series of harmonics above it. You'll need to cancel those out too. Even if you do cancel out the fundamental, you'll still "hear" it because of the missing fundamental effect [1] otherwise. Cancelling those overtones out gets harder and harder because the higher the frequency, the more precise you need to be with phase to get proper cancellation.
3. Obviously, none of this will help with the atonal noise components of the fan's sound, which are significant. Though arguably, if you get rid of the droning tonal part, the remaining whooshing noise might actually be a nice sound.
I believe the most effective fixes here are:
1. Get a better, quieter fan that produces less noise to begin with.
2. Move the fan farther away. You don't necessarily need to filter the air from the window closest to you. Put it in a farther window. Or go all the way and get a whole house fan that puts the fan in the attic.
Is the drone of a fan harmonic? I would’ve thought it’s more like a repetition pitch so its overtones would not be harmonic and would not exhibit a missing fundamental.
Agree with the broader point, just curious if there’s some interesting physics that creates a harmonic sound.
munificent 13 minutes ago [-]
> Is the drone of a fan harmonic?
Overtones are about timbre, not harmony. The fan isn't playing a chord (well, probably not). But the tone the fan plays isn't a pure sine wave either. It will have overtones that are integer multiples of the fundamental that give it its characteristic sound.
It's the same reason that a flute and saxophone can play the same note but sound different. The fundamental is the same, but the amplitudes of the overtones are different.
jerf 3 hours ago [-]
Unfortunately, this is not possible with such a simple approach. In 2 and higher dimensions, the problem is that any attempt to create a cancelling wave from a position other than the source of the wave will not cancel the wave. Instead it will create a network of places where it cancels and places where it constructively interferes, depending on the wavelength and their relative positions, and there is no way to make the entire space be cancelling in such a short space. You can only get various arrangements of cancellation but also constructive feedback.
(Some other things happen as you get a large number of wavelengths away from the source, but given the wavelength of the audio in question, being in a room with it means you get that local behavior, not long-range behavior.)
Probably somewhere on the internet is a fantastic interactive diagram that would clearly demonstrate this for you, but I couldn't google one up. Links solicited. (I got a lot 1D stuff but this phenomenon doesn't show up in 1D. 2D is adequate, 3D just adds more nodes in more dimensions.)
The way noise cancelling headphones work is that they know where they are relative to your eardrum, and as such, they can arrange it so that for all incoming audible frequencies, your eardrum is in a cancellation location for that frequency, ignoring a lot of details. They'll still unavoidably create locations of constructive interference, you just won't have your sensors there.
In principle you may be able to do this with some very precise location of where your ears are, where your mics are, where your speakers are and the exact characteristics of all of these things, and some very clever coding; I've seen people kicking this idea around but I haven't yet heard of anyone pulling it off. I can say it's still yet harder than it sounds at first, because you have things like echos and all kinds of other fun effects to deal with. In theory it should be possible to echo cancel at a distance, but you'd be getting into super high end audio processing, not just a weekend project where you record a microphone or two and "just" invert it with a couple of speakers. You might need something as fancy as https://youtu.be/UPVcwDzhBZ8?t=463 just to get started, and an accurate room model, and all kinds of things, and you might still get something that only works as long as nothing in the room moves, including you or even parts of you. In practice, I'd guesstimate this at the level of difficulty of doing a PhD in audio processing at a minimum... but not necessarily impossible.
NobodyNada 3 hours ago [-]
> Probably somewhere on the internet is a fantastic interactive diagram that would clearly demonstrate this for you, but I couldn't google one up. Links solicited.
The author is focused on beamforming WiFi signals, but the principle is exactly the same whether it's a radio wave or a sound wave.
jerf 3 hours ago [-]
Exactly what I was looking for, thank you.
Interestingly, the wavelength of sound and the wavelength of wifi signals are in the same ballpark. 900MHz electromagnetic waves come out to ~30cm waves, which is about 1000Hz in sound-in-air.
lawlessone 1 hours ago [-]
just my lay person thought here.
But if you could cancel the noise/signal perfectly and everywhere wouldn't that sorta violate energy conservation?
The sound energy has to go somewhere right?
luke-stanley 17 minutes ago [-]
Perfectly? Surely that is not reasonable?
jorvi 2 hours ago [-]
My thought immediately jumped to beamforming / phased speaker array.
What's more problematic is that its not the lower frequencies that are annoying (the 312Mhz drone), but the mid and high range. Think about it like this: fridge compressors suck to hear with their 2500Hz high-pitched electrical buzz, but once the compressor turns off, the gentle but deep slosh of the liquid being pumped around isn't annoying at all.
posix86 3 hours ago [-]
It would be possible if you had a matrix of speakers covering all walls & ceiling. In that scenario you could control the entire sound landscape across the board, and cancel out or simulate arbitrary sound sources in the room.
> The way noise cancelling works is that a microphone picks up the sound-wave, and then another speaker plays a slightly delayed version of that wave, which cancels it out.
I always thought noise cancelling worked by playing an inverted version of the sound wave rather than just a delayed one.
In fact, wikipedia seems to back me up on this:
> A noise-cancellation speaker emits a sound wave with the same amplitude but with an inverted phase (also known as antiphase) relative to the original sound.
If you have a single amplitude wave then a delayed playback could be inversion of the wave. Not very sophisticated, but good enough for canceling a single frequency.
armada651 2 hours ago [-]
The original post stated unequivocally that noise cancellation works by playing a delayed version of the sound before deciding it was only going to cancel a single frequency.
So either the text has been re-ordered or OP is under the mistaken impression this would also work when dealing with a mix of frequencies.
MarkusWandel 2 hours ago [-]
All I know is that decent noise cancelling over-ear headphones (Bose QC35 in my case) are really good at cancelling exactly that sort of noise - the hum plus whoosh of a box fan. Given that they are ineffective for high frequencies but very effective for the low frequency part of the spectrum where most of the fan noise (or airplane roar, or bus engine) is, I also always assumed that they played the least-possible-delayed anti-wave to cancel out the wave. Doesn't work for speech, sadly, since that has enough high-frequency energy to be intelligible even through these phones.
proee 56 minutes ago [-]
This begs the question of what is the most quiet fan(s) on the market? If all of us sat down in a room together and had this mission, what would it look like? An electrostatic fan (using electrohydrodynamics) would be pretty silent, but provide very little airflow. It's a fun problem to solve and would love to see a company create better products than those overpriced Dyson fans (which are junk IMHO).
Theirs probably isn't silent, but you certainly could figure out how to make this very quiet and gentle sounding, building tension in a spring between strokes with some kind of silent linear actuator
asdff 30 minutes ago [-]
Most all ceiling fans I've had make no noise until you are on the "blow all the papers around the room" setting. For the ones that do make noise usually it's merely a balance issue.
rthz 3 hours ago [-]
Interesting problem, not sure it’s worth solving. A larger diameter and slower rotating fan would likely produce less noise for a comparable air flow.
LeifCarrotson 2 hours ago [-]
A 20" Lasko box fan is about as cheap as they come - and, consequently, noisy and inefficient. The thing retails for $20, the budget for quieting measures is $0. In particular, especially when placed at a window (where it's expected to generate a pressure differential) you get a counterflow effect in the corners, and the 5 blades create individual pressure pulses as they move near to the 4 flat sides of the enclosure and then out into open air.
A quality high-volume, low-speed industrial drum or axial HVAC wall fan costs a whole lot more than $20 but the quiet, low-frequency noise is so much less intrusive.
Another mechanism (if you don't want a 36", 1/2 HP galvanized industrial contraption on your desk) is to concentrate the airflow near the user. Less power, but more concentrated. I've got a big fan that helps in the morning and evening to exchange air through the entire house, but on my desk I've got the biggest PC case fan I could find (a 230mm monster) wired to a speed controller cable and then directly to a 12V wall wart. At ~300 RPM, you can almost keep up with the motion of a single blade with your eyes, at 500 or 800 RPM it's barely perceptible... but it's only about 8x8x1" and keeps the air moving over your skin!
asdff 28 minutes ago [-]
Ceiling fans are silent or nearly so in my experience and work a lot better than separate fan units imo.
anjel 2 hours ago [-]
Windows dimensions are a limiting factor to this approach
afry1 3 hours ago [-]
Those Lasko fans have pretty raw edges on the blades of the fan itself, which I think contributes a lot to the noise. If you take the cover off, sand down the nubs and bits of flaking plastic, and reassemble, I think that will take care of a lot of noise.
BizarroLand 28 minutes ago [-]
Blade geometry would make a lot of difference. Could be a fun at home science experiment to do with a 3D printer and $200 worth of filament.
Rooster61 3 hours ago [-]
Is the phenomenon here why when you lay a sound waveform over another which is exactly out of phase copy (try this in Audacity or similar), the final product is silence? Or is that another aspect of sound waves that is similar but not quite the same effect?
drjasonharrison 3 hours ago [-]
This is exactly the physics occuring. Amplitude of sound is pressure. When two signals are 180 degrees out of phase, one is "increases the pressure" while the other "decreases the pressure" of the air.
In an sound editor, the waveforms can be perfectly aligned.
In the physical world, the waveform created by the fan spreads out through space. Providing an opposite but equal sound waveform at your ears is very hard (impossible) with a single speaker but can be done with sound cancelling headphones.
moralestapia 2 hours ago [-]
>can be done with sound cancelling headphones
How/Why?
I guess its because all noise just enters through two holes? So you reduce the dimensions back to 1.
munificent 2 hours ago [-]
Yes.
If you have two speakers playing the same tone (with perhaps different phases), then the distance between you and each speakers will affect the phase at the point that they reach your ears. At different places in the room, the phases will either be out of alignment and cancel out, or in alignment and reinforce. Unless you can literally have both speakers at the exact same position, there's no way have their phase difference be the same across the whole room.
Imagine throwing two rocks into a pond and the way the ripples interact and overlap. It's the exact same phenomenon. If you could throw the two rocks at exactly the same place (and somehow throw a "negative" rock that causes ripples to go up instead of down), then the waves would all cancel out. But if they are in two different locations, you'll get a whole mess of different interactions at different places in the pond.
This isn't an issue with noise-cancelling headphones, because the distance between the incoming sound, the headphone speaker, and your ear is always fixed.
montag 2 hours ago [-]
A more interesting question is probably something like, what’s the quietest (practical) way to move air around the room? My money is on a high-end ceiling fan.
toast0 39 minutes ago [-]
If you have acceptable outside air, and quiet surroundings, and you have both low openings and high openings, you can get natural convection flows that move a good amount of air without much noise. Double hung windows are pretty good for this; you can open the bottom and the top of a single window and get air movement from that. Even better if you have windows on different sides of the room, open the top on one side and the bottom on the other. Typically inside air will escape the top window(s) and be replaced by outside air coming in the bottom window(s), and the moving air at the windows will tend to encourage air movement throughout the room. In a multi-story building with free air movement between floors, you can open windows on the top and bottom floors and get something similar. If that's not enough, using a fan to increase exiting air flow should help.
asdff 27 minutes ago [-]
It doesn't even have to be high end. landlord special is probably fine if it is balanced.
zamadatix 1 hours ago [-]
What I don't get is why the lowest speed on an adjustable speed fan is always so high. It's like if your car could either be parked or go 70-120 MPH. Sometimes I just want a large light breeze, not the papers to fly off my desk.
Aspos 1 hours ago [-]
It is a solved problem for those who can install fans, filters, exhaust and intake valves far away from the room itself and just carry the stale and fresh air via ducts. Always fresh air without noise and mosquitoes.
drooby 3 hours ago [-]
Note - fans should be at least two feet away from the window to leverage the Bernoulli effect
jraph 3 hours ago [-]
I'm interested about this for next summer, could you or someone else expand on this / give pointers?
The fan increases air speed at the centre of the rotor, creating a low pressure zone which then sucks in surrounding air. So it helps to place the fan away from the window (roughly far enough that the wind cone "fits" the opening).
jraph 2 hours ago [-]
I would have loved to see that video 2 months ago. Thanks for sharing.
I tried to put the same kind of desk fan at the window, one way and then the other, for a few hours, to see if it had any effect. It was a very hot day but colder outside than inside. The building's concrete was likely still radiating the heat from the day before and there was no wind.
I see now that my observation at the time was right: it did nothing to the temperature, and it might have worked better if I had put the fan 1-2 meters away from the window, directing it towards the window. Now, whether the effect would have been significant anyway… we'll have to wait for next summer to know, I guess. I'm not particularly looking forward to it, though.
privatelypublic 2 hours ago [-]
A 20 or 24" box fan still moves a LOT of air- you should get a decent breeze if you guide the air. the largest mistake I see is forgetting that a fan can't blow if theres no air coming or going- you need openings of equal size (larger is better) between where the fan is and where you want the air to come from/go.
An easy mental model is imaging the air is water. Close a door on a room and it'll fill up and block the hose.
PS: a box fan and a 5" thick MERV13 filter makes a heck of an air filter. 2" likely also will work. MERV13 is great, but some HVAC can't handle it, and it takes a couple passes (term is air exchanges per hour, I think) to capture what HEPA does in a single pass.
jraph 52 minutes ago [-]
Yep, I had all my windows and doors open.
hettygreen 1 hours ago [-]
You just need a second fan - an exact duplicate of the first, located in the exact same space, but exactly the opposite. This will cancel it out.
rouanza 2 hours ago [-]
Try using a microphone and closed loop generating sound and measuring the result in realtime. Randomly mutating and layering noise to find the best fit.
0xdada 3 hours ago [-]
How would this work without headphones in a room? I'm guessing the noise would actually be amplified in some parts of the room.
quickthrowman 29 minutes ago [-]
If you have a furnace or air handler, it should already be sized to change the air inside a building multiple times per hour which should keep the air nice and clean assuming you change the filters when needed. ‘Change the air’ in this case means the entire air volume of the building passes through the filter, not a total exchange of indoor and outdoor air.
If you want a quiet but expensive solution that doesn’t involve a properly sized air handler, read on.
The solution here is to put the fan outside the building mounted on ductwork that goes inside the building with a damper you can open and close. “Powered roof ventilator” is what you should google.
Then add in a makeup air fan that is interlocked with the exhaust fan (and the dampers on both the exhaust fan and makeup air unit) outside and mounted on ductwork so your house isn’t negatively pressurized which would have the opposite effect, dirt and dust would enter the house. “Makeup air fan” is what you should google.
If you’ve ever been in a commercial kitchen, the vent hood is connected to ductwork that goes outside the building where the exhaust fan in mounted, and there’s always a makeup air unit mounted outside sized roughly the same (cfm) as the exhaust fan to push air into the kitchen to maintain the air pressure and prevent negative pressurization. A (typical modern) large building has multiple intake and exhaust fans that work in concert with a building automation system to maintain air pressure. The idea is to maintain slight positive pressure with respect to the outside air pressure to prevent dust and dirt from being sucked into the building.
jajuuka 3 hours ago [-]
Not very helpful, but an interesting idea nonetheless. Would be interested to read someone who had a working prototype of this.
fluder_tw 3 hours ago [-]
I doubt it can work. Noise cancelling in earphones works good only because it is very narrow ear channel and you are not dealing with any phase shifts due to changing position relative to noise source. Also there is no other things like reverberation and room acoustic which also contributes to phase of the signal that we actually recieve in our ear channel. In other words noise cancellation is possible only in one specific position of listener in the room.
privatelypublic 3 hours ago [-]
Yup. I'm still learning- but it seems like a Helmholtz resonator would be best in this case.
Since a room has reflections and diffraction of the sound waves, the 312hz they're trying to dampen w/ ANC will be at different phases at different parts of the room. It's also not a point source.
fluder_tw 3 hours ago [-]
I would propose funny solution to change the room where 312hz will fall into one of the standing wave frequency. Then if you combine properly where to place fan and where to place your sit, you can achieve effect of cancelling at this frequency/position (and amplifying in other positions)
dmitrygr 2 hours ago [-]
Even if this worked (it will not and cannot), it will only work in SOME places, whereas it will constructively ADD in others since the fan and the speaker are not co-located. To make it work in ALL places you'll need an infinite number of speakers with precise phase control for each. This is how beamforming works. Fun stuff. Mathematically quite a bit more complex than "put a BT speaker near a fan"
Why won't this work even if you could co-locate your speaker with the fan? Fan noise is neither stable in time nor as simple as a sine wave. This would need a complex active system to work.
hopelite 2 hours ago [-]
My first approach would be to experiment with some of the developed low noise blade designs
1. The fan's fundamental frequency isn't perfectly stable, so even if you are in a spot where there speaker's tone cancels with it, the fan will probably wander around that frequency enough that the cancellation won't work well.
2. The fan isn't just a fundamental tone + noise. There are also a whole series of harmonics above it. You'll need to cancel those out too. Even if you do cancel out the fundamental, you'll still "hear" it because of the missing fundamental effect [1] otherwise. Cancelling those overtones out gets harder and harder because the higher the frequency, the more precise you need to be with phase to get proper cancellation.
3. Obviously, none of this will help with the atonal noise components of the fan's sound, which are significant. Though arguably, if you get rid of the droning tonal part, the remaining whooshing noise might actually be a nice sound.
I believe the most effective fixes here are:
1. Get a better, quieter fan that produces less noise to begin with.
2. Move the fan farther away. You don't necessarily need to filter the air from the window closest to you. Put it in a farther window. Or go all the way and get a whole house fan that puts the fan in the attic.
[1]: https://en.wikipedia.org/wiki/Missing_fundamental
Agree with the broader point, just curious if there’s some interesting physics that creates a harmonic sound.
Overtones are about timbre, not harmony. The fan isn't playing a chord (well, probably not). But the tone the fan plays isn't a pure sine wave either. It will have overtones that are integer multiples of the fundamental that give it its characteristic sound.
It's the same reason that a flute and saxophone can play the same note but sound different. The fundamental is the same, but the amplitudes of the overtones are different.
(Some other things happen as you get a large number of wavelengths away from the source, but given the wavelength of the audio in question, being in a room with it means you get that local behavior, not long-range behavior.)
Probably somewhere on the internet is a fantastic interactive diagram that would clearly demonstrate this for you, but I couldn't google one up. Links solicited. (I got a lot 1D stuff but this phenomenon doesn't show up in 1D. 2D is adequate, 3D just adds more nodes in more dimensions.)
The way noise cancelling headphones work is that they know where they are relative to your eardrum, and as such, they can arrange it so that for all incoming audible frequencies, your eardrum is in a cancellation location for that frequency, ignoring a lot of details. They'll still unavoidably create locations of constructive interference, you just won't have your sensors there.
In principle you may be able to do this with some very precise location of where your ears are, where your mics are, where your speakers are and the exact characteristics of all of these things, and some very clever coding; I've seen people kicking this idea around but I haven't yet heard of anyone pulling it off. I can say it's still yet harder than it sounds at first, because you have things like echos and all kinds of other fun effects to deal with. In theory it should be possible to echo cancel at a distance, but you'd be getting into super high end audio processing, not just a weekend project where you record a microphone or two and "just" invert it with a couple of speakers. You might need something as fancy as https://youtu.be/UPVcwDzhBZ8?t=463 just to get started, and an accurate room model, and all kinds of things, and you might still get something that only works as long as nothing in the room moves, including you or even parts of you. In practice, I'd guesstimate this at the level of difficulty of doing a PhD in audio processing at a minimum... but not necessarily impossible.
Here's one: https://apenwarr.ca/beamlab -- as well as the author's writeup: https://apenwarr.ca/log/20140801
The author is focused on beamforming WiFi signals, but the principle is exactly the same whether it's a radio wave or a sound wave.
Interestingly, the wavelength of sound and the wavelength of wifi signals are in the same ballpark. 900MHz electromagnetic waves come out to ~30cm waves, which is about 1000Hz in sound-in-air.
But if you could cancel the noise/signal perfectly and everywhere wouldn't that sorta violate energy conservation?
The sound energy has to go somewhere right?
What's more problematic is that its not the lower frequencies that are annoying (the 312Mhz drone), but the mid and high range. Think about it like this: fridge compressors suck to hear with their 2500Hz high-pitched electrical buzz, but once the compressor turns off, the gentle but deep slosh of the liquid being pumped around isn't annoying at all.
I always thought noise cancelling worked by playing an inverted version of the sound wave rather than just a delayed one.
In fact, wikipedia seems to back me up on this:
> A noise-cancellation speaker emits a sound wave with the same amplitude but with an inverted phase (also known as antiphase) relative to the original sound.
https://en.wikipedia.org/wiki/Active_noise_control
https://graphtoy.com/?f1(x,t)=sin(x)&v1=true&f2(x,t)=sin(x-%...
So either the text has been re-ordered or OP is under the mistaken impression this would also work when dealing with a mix of frequencies.
Theirs probably isn't silent, but you certainly could figure out how to make this very quiet and gentle sounding, building tension in a spring between strokes with some kind of silent linear actuator
A quality high-volume, low-speed industrial drum or axial HVAC wall fan costs a whole lot more than $20 but the quiet, low-frequency noise is so much less intrusive.
Another mechanism (if you don't want a 36", 1/2 HP galvanized industrial contraption on your desk) is to concentrate the airflow near the user. Less power, but more concentrated. I've got a big fan that helps in the morning and evening to exchange air through the entire house, but on my desk I've got the biggest PC case fan I could find (a 230mm monster) wired to a speed controller cable and then directly to a 12V wall wart. At ~300 RPM, you can almost keep up with the motion of a single blade with your eyes, at 500 or 800 RPM it's barely perceptible... but it's only about 8x8x1" and keeps the air moving over your skin!
In an sound editor, the waveforms can be perfectly aligned.
In the physical world, the waveform created by the fan spreads out through space. Providing an opposite but equal sound waveform at your ears is very hard (impossible) with a single speaker but can be done with sound cancelling headphones.
How/Why?
I guess its because all noise just enters through two holes? So you reduce the dimensions back to 1.
If you have two speakers playing the same tone (with perhaps different phases), then the distance between you and each speakers will affect the phase at the point that they reach your ears. At different places in the room, the phases will either be out of alignment and cancel out, or in alignment and reinforce. Unless you can literally have both speakers at the exact same position, there's no way have their phase difference be the same across the whole room.
Imagine throwing two rocks into a pond and the way the ripples interact and overlap. It's the exact same phenomenon. If you could throw the two rocks at exactly the same place (and somehow throw a "negative" rock that causes ripples to go up instead of down), then the waves would all cancel out. But if they are in two different locations, you'll get a whole mess of different interactions at different places in the pond.
This isn't an issue with noise-cancelling headphones, because the distance between the incoming sound, the headphone speaker, and your ear is always fixed.
The fan increases air speed at the centre of the rotor, creating a low pressure zone which then sucks in surrounding air. So it helps to place the fan away from the window (roughly far enough that the wind cone "fits" the opening).
I tried to put the same kind of desk fan at the window, one way and then the other, for a few hours, to see if it had any effect. It was a very hot day but colder outside than inside. The building's concrete was likely still radiating the heat from the day before and there was no wind.
I see now that my observation at the time was right: it did nothing to the temperature, and it might have worked better if I had put the fan 1-2 meters away from the window, directing it towards the window. Now, whether the effect would have been significant anyway… we'll have to wait for next summer to know, I guess. I'm not particularly looking forward to it, though.
An easy mental model is imaging the air is water. Close a door on a room and it'll fill up and block the hose.
PS: a box fan and a 5" thick MERV13 filter makes a heck of an air filter. 2" likely also will work. MERV13 is great, but some HVAC can't handle it, and it takes a couple passes (term is air exchanges per hour, I think) to capture what HEPA does in a single pass.
If you want a quiet but expensive solution that doesn’t involve a properly sized air handler, read on.
The solution here is to put the fan outside the building mounted on ductwork that goes inside the building with a damper you can open and close. “Powered roof ventilator” is what you should google.
Then add in a makeup air fan that is interlocked with the exhaust fan (and the dampers on both the exhaust fan and makeup air unit) outside and mounted on ductwork so your house isn’t negatively pressurized which would have the opposite effect, dirt and dust would enter the house. “Makeup air fan” is what you should google.
If you’ve ever been in a commercial kitchen, the vent hood is connected to ductwork that goes outside the building where the exhaust fan in mounted, and there’s always a makeup air unit mounted outside sized roughly the same (cfm) as the exhaust fan to push air into the kitchen to maintain the air pressure and prevent negative pressurization. A (typical modern) large building has multiple intake and exhaust fans that work in concert with a building automation system to maintain air pressure. The idea is to maintain slight positive pressure with respect to the outside air pressure to prevent dust and dirt from being sucked into the building.
Since a room has reflections and diffraction of the sound waves, the 312hz they're trying to dampen w/ ANC will be at different phases at different parts of the room. It's also not a point source.
Why won't this work even if you could co-locate your speaker with the fan? Fan noise is neither stable in time nor as simple as a sine wave. This would need a complex active system to work.