Comment by munificent | Hacker News Reader

Comment by munificent | Hacker News Reader

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.

[1]: https://en.wikipedia.org/wiki/Missing_fundamental

"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."

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.

> 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.

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.

> 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.

> It will have overtones that are integer multiples of the fundamental that give it its characteristic sound.

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

So are you saying the only difference between a woodwind instrument and a fan is the column? What about a stringed instrument then?

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.

A string fixed at both ends produces harmonic sounds because of its particular structure. In order to have a non-integer overtone the ends would have to move up and down, which by construction they can't. Similarly for wind instruments: the air stops at either end and is reflected back, and a non-integer overtone would require changing the length of the tube (or sticking holes in it to allow the pressure to go to zero at the hole, effectively creating an artificial "end" of the tube).

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.

> why would the overtones go in integer multiples (I.e. be harmonic) for a fan?

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.

This is just math, not physics. Suppose you have a thing vibrating in a periodic manner. You might imagine that it will vibrate the air so that the sound pressure is some periodic function of time. Fourier transform that function to get a spectrum, and it will have discrete peaks at the fundamental frequency (1 / period) and at integer multiples of that frequency. You don’t even need to decompose into sine and cosine functions for this to work — all that’s really going on is that you have f(t) = f(t + period), and you’re turning f into the sum of a bunch of other functions g_1, g_2, etc, all of which have the same property that g_i(t) = g_i(t + period). Of course, if a function g has the property that, for all t, g(t) = g(t + period/n) for any integer n, then you can iterate that property n times and you’ll also have g(t) = g(t + period). And these functions with the fundamental period, half the fundamental period, one third the fundamental period, etc, are the fundamental tone and its overtones. You could decompose into square waves or just about anything else and you would get the same result.

(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.)

It's the nature of resonance and vibration.

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).

Your question displays sufficient knowledgeability of the phenomenon of strictly integer harmonics, that you can basically disregard the replies explaining how they could arise, whereas your question is more about given that it shouldn't arise inevitably, how do we know they would be harmonic given the case of a fan.

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.

Please downvote this comment. But I had to say thanks for this. It's one of the litte glistening ornaments on the perennial HN xmas tree. Good thread (and post) altogether.

The nature of the full spectral sound is not really the point.

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.

I wonder if it wouldn't be better to have two fans: one at a high position and one at a low position.

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