Hio my friend: I think that we are having a bit of divergence on the origin and description of sound.
A) Sound is a "reactive" product. By itself, it does not exist except as the result of another action creating the particular frequency that is discernible by whatever means, organic (life) or instrumental as sound..
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B) Sound blends into the other frequencies, there is no clear cut frequency that is considered as sound, unless you define the actual receptive device.
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C) You stated --> all matter that adds substracts divids and multiplies creates sound,.
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Agreed in principal, a reactive result. - see "A"
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D) You posted --> these sound wave are a fundmental sine sound wave
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?? fundamental

They must by definition, be a harmonic of THE fundamental - the Universe's, nature.
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E) You posted --> these hormonics convert sound waves into a cohesion of two waves working as one
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Agreed, at various points in the frequency range, which is effectively infinite, all do.
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F) You posted -->these hormonics convert sound waves into a cohesion of two waves working as one
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To a point agreed, but what about the other infinite no.of waves which are "out" of phase with them?*************************************************************************************
G) You posted --> adding subtracting dividing or mutlipling must apply to the 5th element of sound
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What is the fundamental frequency of sound ?
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H) You posted --> that's why we hear thunder yet lighting only takes place after sound
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Hmm, since sound is strictly an infinitely, variable, " reactive" frequency --- hmmm.
Speaking personally, when a bomb or shell explodes, the resulting pressure breaks up the casing into many smaller parts which travel outwards faster than the perceived sound. I have received some of these fragments before the sound of of the chemical reaction - explosion - reached my ears.
In the case of lightning, it has been proven in the laboratory that the energy in the lightening heats up the air to a point that it is practically non-existent though expansion, then as it cools, the resulting collapse, and in rushing cool air, creates the presssure wave of "sound"., Actually there are two pressure waves which are produced by the lightning, the expansion phase and the collapsing one, not the reverse.
Don Jose de La Mancha