Noise cancelling a fan
chillphysicsenjoyer.substack.com
chillphysicsenjoyer.substack.com
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.
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."
This might work for homeowners, but is an ineffective solution to renters like me. Our furnace/air conditioning blower is loud AF. The utility closet is next to the bedroom and it is nearly impossible to hear the TV when it is running. It is so loud that we even have to turn up the TV in the living room, around 25 feet (7m?) away and around two corners. I am CERTAIN that other renters, like myself, would like to know how to actually cancel out this droning nuisance via noise cancellation.
Objecting to the proffered solutions doesn't make the unworkable one workable.
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.
What I’m wondering is why would the overtones go in integer multiples (I.e. be harmonic) for a fan? A flute and a saxophone have harmonic(ish) overtones because of the physics of a vibrating column of air
(In any discussion of Fourier transforms complete with equations, you’ll usually see a bunch of factors of 2π because the frequencies are angular frequencies. This is done for mathematical convenience and has no effect on any of this.)
Some of the replies pontificate and assume sounds are periodic, and hence their harmonics must have been perfectly integral, which is of course totally bonkers.
Yes, some instruments are harmonic (i.e. integral harmonics down to ~ ppm frequency ratio errors) like violins, but only because those are bowed strings, resulting in phase locking.
Plucked strings are much further from integral harmonics, due to dispersion: yes standing waves for a frequency-independent wavespeed c on the string would give perfectly harmonic partials. Real strings show dispersion (a frequency dependent wavespeed) resulting in inharmonic partials.
Nothing indicates fan noise to be strongly harmonic. Their composite sound may have structured and repeatable (in)harmonic components in many ways, harmonics would be easiest to explain. The part that sounds "white" would presumably be hard to characterize and cancel.
If the fan has any recognizable pitch at all, it's because something periodic is happening. If it's loud enough to be annoying, there's probably some resonance going on to amplify it.
For example, maybe the motor spins at 120 Hz, and it's slight asymmetry shakes the chassis of the fan. That shaking will send waves across the body of the fan. Any of those waves whose wavelength is not an integer multiple of the size of the body will bounce around and end up destructively cancelling out. But the wavelengths that are at are close to integer multiples of the resonating frequency of the body will reinforce themselves as the bounce back and forth across the chassis and get amplified.
If you do an image search for "string overtones", you can get a picture of what I mean. Random physical objects aren't all strings, but many of them have at least a little plasticity and rigidity such that they can vibrate and resonate. When they do, the result will be harmonics at the object's fundamental frequency and integer multiples.
Other frequencies occur too. If you strike a bell, for example, that impulse will produce waves at basically all frequencies. It's just that the ones that don't resonate with the bell's fundamental will cancel themselves out and fade out nearly instantly (that's the clanky part of the very beginning of a bell sound). The multiples of the resonance frequency will ring out (the bell-like peal that decays slowly).
Every sound found in nature contains multiple frequency components. When these align as integer multiples of the fundamental, they are harmonics; when they do not, they are inharmonic partials. Only a pure sine wave lacks them, and such signals don’t occur naturally.
By contrast, a freely vibrating bar (not fixed at the ends) does not have harmonic overtones. To make the bars of a xylophone, marimba, or vibraphone sound nice, you have to cut out a little "scoop" shape from the bottom of the bar to force it to vibrate such that its overtones match up with integer multiples of the fundamental frequency of the bar.
As you say, most sounds in nature do not have a harmonic spectrum, so if a fan did I would find that surprising and interesting.
The fan noise is from its own vibrations -- presumably driven by the motor. These vibrations will correspond to natural vibrating modes on the body of the vibrating object -- which could be the motor, or the chassis, or even possibly the fan blades. Whatever the shape, the natural modes will be naturally quantized into "harmonics". Those vibrating modes could have more nuanced spatial forms (eg. Bessel functions) but their temporal pattern would likely be sinusoid.
Where is the majority of the energy? Probably in the harmonics. Remove them, and you've severely reduced the noise.
How to do this, is the problem.
(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.
You'd have to run realtime 3-D FFTs on the sound in the system, at approximately a few kHz.
I guess the 'fan as the noise cancelling speaker' idea could be reworded as 'a fan with active stabilization that doesn't vibrate', making no mechanical noise.
A friend with a recording studio solved their problem by putting the fan at the end of a length of ducting with a couple of 90 degree bends, lined with foam.
1. use the Bernoulli-Effect, aka get "up to 50+%"(depends on fan model) more airflow by placing the fan 0.2(0.5) - 1.5m away from the window.
2. Blow air out of the window, dont try to suck air in.
3. To avoid noise: Put the fan in another room and open the window in the room where you are.
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://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.
There is no discernable difference between a phase-shifted tone, and a delayed tone, except for the initial period where the tone begins.
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!
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
I once knew a rogue architect who rode a bicycle, wore broken glasses mended with tape and lived in a home in south Florida (warm humid summers). He had dug trenches beneath his house, which he explained were for air circulation intended to work in harmony with interior modifications which I can't remember.
Unfortunately the city condemned and demolished his house. But I've been intrigued by solid state cooling methods since. The Japanese fan, though of questionable mechanical efficiency, ispires me as an example of easily overlooked but formidable design. Neat!
That's intriguing. Along those lines, I've also been interested in the idea of using pressure sensors and anemomenters to automatically open/close different windows in my house to create optimal airflow. Unfortunately the house I'm in is 100 years old, so for now it's just a daydream.
I wish you a meantime epiphany that fits if the master plan won't do.
Essentially they make the same sound, but 100's of times lower in audible volume, just as they move 100's of times less volume of air per second. (It may not be linearly scaled, but it's definitely proportional.)
This was an experiment in my high school physics, where our teacher played a constant tone from two sources and students were to walk around the class room searching for dead spots where the phases would cancel each other out.
It was quite surreal to take a step and suddenly the tones went quiet.
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.
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.
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.
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.
Instead, it's probably a better idea to not create the noise in the first place.
PS: Typed while wearing a pair of fairly tattered Bose QC45 1st gen because I'm intent on repairing perpetually rather than $$$ replacement.
It had an on-off controller, and I replaced with a smooth pid controller. Now when it starts making noise it's making much less noise and much earlier. And mostly stays below 20%
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.