Spoiler Scope Preface

Please spoiler tag anything that happens after Part IV. My intention is to discuss anything up to the end of Part IV here, since I've only read the first chapter of Part V so far.

Disclaimer

I'm not one of those people who has every WOB and every cosmere fact memorized, so hopefully I don't overlook something in this discussion that makes it all moot.

tl;dr

Either Navani doesn't actually fundamentally understand how she made the "anti-tone" to expel Voidlight or Sanderson is getting a little too cute with physics.

Cosmere Physics

As far as I recall, in the cosmere, the standard laws of physics all exist, PLUS there is an extra thing called investiture. Instead of just having mass/energy conservation, we now have mass/energy/investiture conservation. Although I have a background in physics (PhD in experimental condensed matter physics), I'm not very strong in topics like fundamental symmetries in quantum mechanics and high energy / medium energy physics. But I'm quite confident that physics would pretty fundamentally be different in the cosmere because of this extra piece. My intention is not to get into the weeds of that. I love the investiture system and really appreciate that Sanderson tries to tie it to physics. I like that it is meant to be rooted in some sort of fundamental physics, but allows for a lot of wiggle room. I don't expect it to be legitimately explainable with a technically sound rederivation of physics that includes investiture. So I will assume that the laws of physics are essentially the same in the cosmere, and that investiture by and large is decoupled from the rest of physics.

Navani's Experiments

I suspected for some time that something akin to interference would be the key to "anti-Light" given Sanderson's proclivity to use as much "real" science as possible in his works. But I expected it to be related to optical interference and maybe wave-particle duality (Navani's musings about Light sometimes behaving like gas and other times like liquid stood out as a parallel to normal light having some wave-like and some particle-like properties). It seems like Light is Investiture Connection, which will determine if it is Stormlight (connected to Honor), Lifelight (connected to Cultivation), or Voidlight (connected to Odium). The Investiture seems to exist in its raw form as a light-like substance, and the Connection is made via sound, with each shard having a "pure tone" associated with it.

Thanks to help from Raboniel, Navani learns that Light can be "pulled" using its associated tone. She thinks about this as a "positive" sound, and postulates that there should be a "negative" sound that is its opposite, which should disperse Light. There is some interesting exposition about the state of physics understanding on Roshar as Navani thinks through some concepts she is familiar with. We also learn that she has likely been exposed to a very broad range of engineering subjects but is not an expert in all of them. It also seems that Rosharan engineers are not as well versed in some areas that we consider to be very basic, based on Navani's perspective on "sound theory":

The opposite of most numbers was a negative number. Could a tone be negative? Could there be a negative wavelength? Many such ideas couldn't exist in the real world, like negative numbers were an artificial construct. But those peaks and troughs ... could she make a tone that produced the opposite pattern? Peaks where there were troughs, troughs where there were peaks?

During her feverish study into sound theory, she discovered the answer to this. A wave could be negated, its opposite created and presented in a way that nullified the original. Canceling it out. They called it destructive interference. Strangely, the theories said that a sound and its opposite sounded exactly the same.

Any engineer on Earth would be immediately familiar with these concepts, as they are covered in intro physics. But importantly, this is a completely accurate depiction of wave interference. However, Navani proceeds to create the anti-tone in a way that is not consistent with the physics of wave interference. She modifies one of the plates by filing pieces of it away (details not provided) until it produces the tone she hears in her head, and indeed it worked. It pushed voidlight out. But modifying the plate could not feasibly create destructive interference. It would change the resonant frequency of the plate, which would change the tone. In fact, as I will explain, destructive interference is not something that can really be achieved with a universal "anti-tone" to an existing tone.

Real Destructive Interference

The tl;dr of this section is that destructive interference requires at least two coherent monochromatic sources, and it is generally an effect observed at discrete points in space except for special cases.

Waves observe superposition. This means that when multiple waves overlap, you can treat this combination of waves as the simple sum of the constituent waves. For example, if wave A has a value of x at a particular location at a particular time, and wave B has a value of y at that same location at that same time, then you get x y. For well-defined interference to occur (meaning it is sustained and observable in a meaningful way), the wave sources must be monochromatic and coherent. "Monochromatic" is the technical term for a wave with a single frequency. Presumably, the Rosharan tones are monochromatic, because they are described as being "pure" tones. "Coherent" means there is a fixed phase relationship. This is not a fundamental property of a single wave, but rather relationship between multiple waves. It means that the relative position of peaks and troughs is fixed. An example of an incoherent light source would be a lightbulb, where all of the "rays of light" coming out of it have random phase. A laser, on the other hand, is coherent. If you've ever wondered why laser light looks speckled on a wall, this is due to interference of the coherent light after it reflects from the roughness of the wall. Light from a light bulb, on the other hand, does not exhibit this effect.

So how would you get destructive interference in real life? One easy way is to have two coherent sources of sound that are in phase with each other (at the location of the sources, troughs and peaks are generated at the same time at one source as at the other source). On modern Earth, this can be accomplished with speakers. In theory, you could also get two in-phase tuning forks by exciting them at the exact same time. But even two identical tuning forks will be coherent and monochromatic regardless of how they're excited (they just won't necessarily be in phase, which would slightly complicate the very simple math discussed below). If we define r1 as the distance from Source 1 to some point of observation, and r2 as the distance from Source 2 to that same point of observation, then at all points in space where |r1-r2|=λ(2n 1)/2 you get destructive interference, where λ is the wavelength and n is any integer. In other words, where the difference in distance between Source 1 and Source 2 is an odd half integer multiple of the wavelength. At these locations, you get a peak from one source and a trough from the other source, and they cancel out. You can read a little more about this here. The important takeaway is that destructive interference is a phenomenon that requires at least two monochromatic coherent wave sources and it occurs at a discrete locations that are determined by the relative distance from the two wave sources (and in the more general case, also the relative phase between the sources). In other words, there is no such thing as a universal "anti-tone."

Why Navani's Discovery Doesn't Make Sense in Terms of Destructive Interference

The fundamental premise behind how Navani pushed voidlight out of the gemstone is inconsistent with destructive interference. If the metal plate normally makes Odium's pure tone, modifying it with a file would simply change its resonant modes. This would change the tone that it creates, not change its phase relative to the gemstone. The correct experiment would have been to have a tuning fork that produces Odium's tone and move the gemstone in a straight line away from the tuning fork. At certain locations, the gemstone would be out of phase with the tuning fork and you'd get destructive interference [edit: I'm assuming what's "supposed" to be happening in Navani's experiment is the sound produced by the plate is interfering with the gemstone's own sound; the gemstone is in that sense both the second sound source and the point of observation]. This experiment would in practice have different results every time it was repeated because it would be impossible to excite the tuning fork with the same phase relative to the gemstone's voidlight each time. So the locations of destructive interference would be different each time you struck the tuning fork again.
There is pretty clearly some Intent fuckery going on with the "anti-tone," which means the rules of investiture are at play. So I am giving the benefit of the doubt to Sanderson here that Navani is somewhat of an unreliable narrator when it comes to why her experiment worked. It just stuck out to me that Sanderson used a very accurate explanation of Earth-universe destructive interference and then had Navani do an experiment that was completely inconsistent with it.