Topology of points

[DoYouKnow]

h(r) in the spherical wave equation
phi = g(r-at) + h(r+at)
is equivalent to an extra coordinate of a point which represents intensity (think of it as brightness), and varies with time.
(x_1, x_2, ... x_n, h(r))
The intensity corresponds to the radius of the spherical wave. (Since radius dependent on distance in calculating brightness).
In function notation a singularity occurs at 1/x, for x=0, because it is not defined.
The limit however is, lim x->0 1/x = infinity.
The behavior of a function is odd at places where the denominator or numerator equal 0.
Since singular points occur in general relativity and point masses/charges are common in classical mechanics, I think it's important to understand more about the point.

[dleviwing]

DoYouKnow;
I'm not sure what you are pointing out here. Are you referring to phase velocity, scattering, or something else? You seem to be missing some variables to the spherical wave equation even in its simplest form.
http://galileo.phys.virginia.edu/classes/252/Classical_Waves/Classical_Waves.html
http://scienceworld.wolfram.com/physics/MieScattering.html

[DoYouKnow]

Hi,

Yes, you're probably right. I like that site on the different wave equations. Thanks for the link. The functions f and g already represent the amplitude, so I think me taking out that part of the function and inserting it in the coordinates for the point was unjustified. I was referring to the 1-dimensional wave equations with the waves as circles emanating from a point (like a pebble thrown into a pond) rather than across a 1-dimensional string. http://scienceworld.wolfram.com/phys...ricalWave.html . But I do think that the wave equation is important, since it seems to relate point particles with their interactions in continua.

[dleviwing]

But I do think that the wave equation is important, since it seems to relate point particles with their interactions in continua.

DoYouKnow;
I agree completely. Understanding the functions of matter waves and the interactions they cause is a key fundamental to comprehending the forces of nature. This site should interest you if you haven't been there already.
http://www.quantummatter.com/