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Incubator Q&A

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Incubator Q&A How many megahertz of vibrations would it take to Shatter solid rock

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 vibration...

posted 14d ago by Olin Lathrop‭

Answer
#1: Initial revision by user avatar Olin Lathrop‭ · 2024-11-07T18:01:39Z (14 days ago)
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.