The resonating sword of doom

Background info:

Jack is back and his first opponent proved, that TARTAKOVSKY IS STILL THE KING OF STORYTELLING and characters and visuals.

Basically, I want to make something similar to the weapon of Samurai Jack's first real opponent (Scaramouch) from the fifth season.

We know:

• This weapon can't be effectively held against elastic things (like Jack's skin)
• Before the usage of its main attack, it needs to "sample" the material, we want to explode.
• Its power is directed and takes some time until the explosion, this time's length can vary
• It's known, that this weapon operates with soundwaves and frequency.

Further information can be found here.

Question

Would it be possible to make such a weapon? If yes, then what would be its limits?

• Part of what makes Samurai Jack such a good show is their constant willingness to let aesthetics win out over reality. Commented Mar 21, 2017 at 20:44
• @sphennings Yep, that's true. Commented Mar 21, 2017 at 20:51

The idea of destroying things by tuning to their resonant frequency is well known, and even works in some cases. However, the totality of the task at hand is more complicated than that.

The idea behind destroying something by emitting sound at its resonant frequency is to transfer energy into the system at a "resonant" frequency, which is one that the material naturally continues to oscillate at rather than bleeding the energy off into some other form like heat. Any medium that is behaving elastically (like glass) has a resonant frequency which can be calculated from its properties.

The destructive bit arises when the energy reaches a point where non-linear effects start to take effect. In the case of a glass breaking, its because bonds get broken at the region of the highest stress and that causes an avalanche like effect which destroys the material. However, this is not the only non-linear effect that can be achieved. Any system wastes energy into heat. No system is perfectly elastic. As an example, a glass that is tapped, causing it to ring, will eventually stop ringing because the energy is emitted into the air as sound vibrations. You need to put enough power into the system at that resonant frequency to reach catastrophic effects before the object under attack can bleed the energy off into heat or emit it elsewhere.

In the case of a glass, this can be done with a simple loudspeaker. The loudspeaker can generate enough power to overwhelm the attenuation of the glass and cause it to reach its breakdown point. In other cases, you may need much more power. Galoping Girdie famously collapsed because the wind was capable of causing the bridge to resonate wildly enough to break down. That took more power, though. It took a mighty 42mph sustained wind to take her down.

Modern engineered products tend to be aware of such effects and are designed to be immune to them. We have many ways to bleed off vibrational energies into heat before they become an issue. For example, you may have seen these little guys on power lines:

They're called Stockbridge dampers and they're designed to stop a catastrophic failure of the wire due to a resonance associated with the wire rolling in the wind. They are tuned just out of tune with the wire so that they couple strongly with the wire and then turn that energy into heat as they change shape. This bleeds resonant energy off of the wire so that it doesn't fail.

In theory you can still attach such a system by attacking the GCD of all of its frequencies. If you have an object that resonates at 500Hz and it is coupled to an object that's tuned to 495Hz, you can still cause the whole system to resonate at 5Hz. However, this can quickly lead one into a region of frequencies where the assumption that materials are elastic is not so valid. If you have many many coupled resonators together, their common resonant frequency might be thousandths of a hertz. As you get into those ranges, the elastic assumptions get tricky. More and more of the energy can get turned into heat by inefficiency. This is why you can't find the resonant frequency of a human and have them explode.

Well, you could, but it would involve pumping enough power into the system to overwhelm our ability to dissipate that energy as heat. At those frequencies, you might as well stop thinking in terms of loudspeakers, and start thinking in terms of hitting them with a baseball bat!

Or a sword! Swords are very good at this sort of thing!

• What would happen if I were to resonate a small part of the material with this? Commented Mar 21, 2017 at 21:21
• That would help you couple your speaker to the specific part you want to resonate, which decreases how much power you have to waste during the process. Other than that, the effect would be the same. Your small piece would resonate within the larger body of the object, generating heat if there were any mismatches in resonante frequency. Commented Mar 21, 2017 at 21:26
• So, I have to: 1. find the frequency 2.overload the material with kinetic energy asap with miniature explosions? Commented Mar 23, 2017 at 14:52
• As a technicality, yes. However, to do it using resonance you have to put all your energy at that frequency, which may be so low that the process may take eons. If you try to put all the energy in really quickly, that energy is actually spread out across many frequencies (there's some math behind that statement, but it involves calculus). You have to do it slowly and patiently. In practice, hitting it with a hammer until it stops functioning is vastly more effective. It's why we have hammers. Commented Mar 23, 2017 at 15:46

No it's not possible to make a weaponized tuning fork.

In perfect laboratory conditions on materials prone to shattering ie. glass it has been possible to shatter materials using their resonant frequency.

Getting arbitrary objects to explode just by tapping them in an object the size of a knife is pushing the bounds of impossibility.

• Seems legit. After all, it would still require something similar to a (specialized) speaker. Commented Mar 21, 2017 at 20:43
• There's no speaker shown. Since it's used by Jack in the next episode after he has been stripped of most of his clothes, we can assume that the blade is the totality of the device. Commented Mar 21, 2017 at 20:45
• Then let's just assume for a sec (purely hypothetically), that Jack had something else with him, ok :) I'm just curious. Commented Mar 21, 2017 at 20:48

No, you're not going to be able to make things explode using their resonance frequency. The resonance frequency is not something magical - it is just something that allows you to add more energy into a system while minimizing losses.

Consider a swing that a child is playing with. Did you know that the swing has a resonance frequency? It's the time it takes to go one way and then come back. If you know how to, you can add energy a little bit at a time and end up swinging pretty high. With a sufficiently large swing, you could easily get 3 meters off the ground, higher than the current world record high jump.

Resonance frequency works the same way in other objects - if something has a resonance frequency, you can use that frequency to continue adding energy to the system. However, you'd never get an explosion because of this. Because you're gradually adding more and more energy to the system, eventually the system will reach a point at which the weakest part will no longer be able to withstand the forces on it. When that part breaks, the resonance frequency will almost certainly change, so the rest of the system will survive. The best case scenario for your sword of doom is that the entire target is of a uniform strength, and the entire thing would shatter.

An interesting case of resonance frequency wreaking havoc is with the original Tacoma Narrows Bridge, "Galloping Gertie." Due to lack of proper damping systems, it had a resonance frequency that the winds would sometimes hit. So one day a storm with the right wind speed lasted long enough that the bridge eventually collapsed. If you watch a video of the collapse you'll notice a some interesting things. First, it was not quick - it took an hour of intense swinging for the bridge to collapse. Second, there was a lot of energy in the system - the bridge was moving a lot. Third, the bridge did not explode - it shook itself apart.

There's a new bridge there, now, that doesn't gallop. The reason it doesn't gallop is another reason why your sword of doom isn't plausible - damping. Bridges that have built since then have parts in place that can absorb extra energy, effectively eliminating the object's resonance frequency. You've probably personally experienced this as well - if you're holding a piece of metal and hit it against something, it won't ring for very long. That's because your hand damps the energy in the metal.

So unless Scaramouch's sword had a ridiculously powerful energy source, realistically Jack's dagger would have been protected from it just from Jack having it in his hand.