Acoustics Engineering, Mind, and Implicative Truth Synthesis

Vibrating piston and induced oscillation of elastic air. Air is elastic as you can verify with a simple experiment - block the hose of the bike tire pump and push the handle. You will notice that the compressed air behaves like spring (Beranek, Acoustics).

Changing pressure in the air is investigated and analyzed within acoustics engineering. However, there is n no engineering link between engineering loudspeaker or vibrating piston and the mind's interpretation of the sound as music. Unless you consider Implicative Truth Synthesis direction of thinking. Pressure analysis in the air stays within the realm of engineering.

For instance, in acoustics engineering or loudspeaker design, the principal concept is pressure. Invention concept is linked to the diaphragm of the loudspeaker moving back and forth thus producing variation in air pressure in front of it, and since air is elastic medium, the wave motion is transferred at the distance, to the ears of listeners where it activates air pressure receptors sending signal to the brain where it is perceived as music. The pressure is physical link between physics and psychoacoustics. Theorems in the pressure domain are axioms or postulate or starting premises for pressure receptors whose theorems are axioms for neurons who further transfer the signal to the brain where it is represented or interpreted as music.

Musicians deal with pressure frequencies. Music composition is, therefore, in the realm of human's musical creativity. The voice or musical instrument that produces air pressure variations aimed at the microphone is the axiom or postulate generator for the microphone membrane (diaphragm). What is a complete theorem in the musical composition or song is the starting premise for the microphone. This postulate that can be seen to be given a-priori to the microphone propagate further through the transduction in the microphone from mechanical to electrical signal to the amplifier and further to the voice coil to the loudspeaker's diaphragm to the elastic air to the ear of listeners to the ear's pressure receptors to the neurons to the brain where it is interpreted as music. At each of these stages theorem-axiom pair is in action. What is theorem in the former is the axiom or postulate for the latter.

There is no concept of frequency in music without elasticity of air. This property is in the centre of the acoustical engineering. The air pressure varies in the sinusoidal fashion and therefore can be analyzed with Fourier Transform. Because of the elasticity of air, the Fourier analysis is possible. As expected, Fourier Transform can be developed in pure mathematical way, by postulating certain sets and sets configurations. But, these set elements postulates can come from another discipline, like heat engineering or  physics. 

With Implicative Truth Synthesis you link any discipline that can generate sets via the mathematics' principal concept of  "is a member of  (a set)", "is an element (of a set)", or "belongs to (a set)" to mathematics and use mathematics results in that discipline. The "what is theorem in one system is an axiom to another linked system", you can link multiple disciplines together. That's how multidisciplinary teams function.

Read more about a powerful reasoning method, Implicative Truth Synthesis in my book, "Yes, You Can!".