Tuesday, June 10, 2008

Differential equations

Differential equations are used to be written mathematically the relationship between the velocity and the position of a particle. I'm interested in the case when the position of the particle is perturbed from time to time instantaneously (the duration of the perturbation is negligible small). Recently, I'm interested in the investigations when the time of these perturbations are at random moments. Think about a pendulum that hits an obstacle at random moments. Will it be stable?

I hope I gave you understandable explanations about DEs.

That is a great explanation of differential equations for me.

I use the formula V = f*w
V = the speed of sound through air, water, etc.
f = frequency
w = wavelength

I use this formula so that people can measure their rooms in length, width, and height and then find the frequency in Hz or cps and know what musical chords are inherent in their room.

I also used the formula to determine the frequency of different blood cells based upon their dimensions ( I think in was in microns) and the velocity was the speed of sound in salt water. I wrote a paper on this in the 80's.

The "dimension" is what I used rather than the "position" in this relationship of sound and its velocity, frequency and wavelength.

The only way I used time was in calculating the frequency of the planets using seconds, minutes, hours, days and years to determine their frequencies. I then used Helmholtz's table of ratios to see if the planets would confirm some of the ratios in his table and they did correspond! I briefly showed this in my Power Point presentation in Plovdiv that you saw. I also determined the frequencies of light years, isotopes etc. and have translated some of these into both musical notations and colors.

Do you think that I could use differential equations in my work with musical intervals, color, frequencies and ratios?

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