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How many megahertz of vibrations would it take to Shatter solid rock Question
Backstory:
I had an idea of someone who can generate powerful vibrations that can either be used to amplify physical attacks or fire these vibrations in a direct oscillating stream for ranged attacks. In addition he has superhuman durability so his own vibrations don't kill him, but his main trait is his ability to use these vibrations to dig underground at a rapid rate by shattering and granulating the materials beneath him, with much of his vibration abilities being based on Shara Ivalda from monster hunter. Now as I was coming up with this character I started to look into vibrations and as I looked into the possible science of how this could work I eventually started to end up in a dead end when trying to figure out how many megahertz it takes to do stuff like this.
Question: How many megahertz of vibrations would it take to granulate solid rock for greater digging abilities.
1 answer
The frequency of the vibrations is only one of many considerations.
To "granulate" rock, the vibrations have to cause large tension forces in the brittle material. The wavelength of the vibrations gives a rough idea of the size of the resulting pieces. Pieces much smaller than a wavelength vibrate all as one, so don't build up the large tension forces inside.
To get the wavelength, we need to know the speed of sound in the material. Just "rock" is not very specific. The fastest earthquake waves travel at about 8 km/s, so let's go with that. That means 8 kHz has a 1 m wavelength. Let's say you want a wavelength of 10 mm, so you need 100 times that frequency, which is 800 kHz, or roughly 1 MHz.
Of course the power needed will be large. And then there is the problem of how to actually produce mechanical oscillations with large displacements at 1 MHz. Even if you manage that, your "small" being somehow has to couple those vibrations into solid rock with much larger mass. There is a serious impedance mismatch.
The process will likely be quite inefficient, both in producing the vibrations and in their ability to fracture rock. Most of the power will go to heating the rock. If you can restrict the spread of the vibrations in a plane, then their power "only" attenuates with the square of the distance. For real 3-dimensional rock, the vibration power diminishes with the cube of the distance. Beam forming and steering will help a little with focusing the power in a particular direction, but the 1/cube law still applies to any beam.
All in all, this sounds really implausible.
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