3 micrometer (radius) scattering	12 micrometer (radius) scattering

Air Resonance radius 3 = 1.1 MHz        Air Resonance radius 6 = 530 kHz
(typical albumen testing bubble)

________________________________________________________________________
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
 . . . . . . . .  For a gas with c = 343 m/s (air) . . . . . . . . . . .
. . . . . . . .         (hard sphere in air)      . . . . . . . . . . .
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
	
ka =  1    gives    f =  18 MHz		ka =  1    gives    f = 9.1 MHz
ka =  2    gives    f =  36 MHz		ka =  2    gives    f =  18 MHz
-------------------------------		-------------------------------	
ka =  5    gives    f =  91 MHz		ka =  5    gives    f =  46 MHz
-------------------------------		-------------------------------	
ka = 10    gives    f = 180 MHz		ka = 10    gives    f =  91 MHz


1   MHz    gives   ka  = 0.055		1   MHz    gives   ka  =  0.11		
2   MHz    gives   ka  = 0.11		2   MHz    gives   ka  =  0.22		
-------------------------------		-------------------------------	
10  MHz    gives   ka  = 0.55		10  MHz    gives   ka  =  1.10		
-------------------------------		-------------------------------	
100 MHz    gives   ka  = 5.5		100 MHz    gives   ka  =  11		



 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
=========================================================================
=============    For a fluid with c = 1500 m/s (water)   ================
. . . . . . . .         (hard sphere in air)      . . . . . . . . . . .
=============         (for an air bubble in water)       ================
=========================================================================


ka =  1    gives    f =  80 MHz		ka =  1    gives    f =  40 MHz	
ka =  2    gives    f = 160 MHz		ka =  2    gives    f =  80 MHz	
-------------------------------		-------------------------------	
ka =  5    gives    f = 400 MHz		ka =  5    gives    f = 200 MHz	
-------------------------------		-------------------------------	
ka = 10    gives    f = 800 MHz		ka = 10    gives    f = 400 MHz	


1   MHz    gives   ka  =  0.013		1   MHz    gives   ka  =  0.025  	
2   MHz    gives   ka  =  0.025		2   MHz    gives   ka  =  0.050  	
-------------------------------		-------------------------------	
10  MHz    gives   ka  =  0.13 		10  MHz    gives   ka  =  0.250  	
-------------------------------		-------------------------------	
100 MHz    gives   ka  =  1.3  		100 MHz    gives   ka  =  2.50  		









ka_i  =  2 pi (radius in microns) (freq in MHz) / (c in meters/sec)
f_i   =  (c in meters/sec) (ka) / 2 pi (radius in microns)
ka    =  (2 pi / wavelength in microns) * (radius in microns)