Kramers-Kronig relationship between ultrasonic attenuation and phase velocty

[chauhan89]

Hi Forum,

I am currently attempting to utilize http://bayes.wustl.edu/etj/articles/kramers-kronig.pdf" Unfortunately ... I have not been successful. I have tried for the past week and asked those around me.
All help is appreciated.

The equation is as follows:
( 1/c(w0) ) - ( 1/c(w) ) = 2/pi*( integral from w0 to w ; wrt dw')

the integrand is
alpha(w')/(w'^2)

Definitions
alpha ;known function for attenuation.
c ;function for speed
w0 ;known base frequency, speed known at this frequency
w ;variable frequency (chosen by me; I would use equation to solve for c(w) )

I believe the problem lies with the units I use for attenuation.
Attenuation data that is available in db/cm does not provide the correct results. This happens when I keep the attenuation in db/cm or do a conversion.

ie. A is db/cm. I use the value ==10^(A/20).

I do get correct results when I use attenuation data available in cm. (no db or anything).

So is my conversion wrong? Is there another way to treat attenuation? I have tried variations such as 10^(A/10), and made sure MatLab numerical integration is accurate, other unit conversions accurate, etc.

All help is welcome! :)

 

[cesiumfrog]

How are you able to tell whether your results are correct? Where are you obtaining the different types of data?

 

[Born2bwire]

You obviously shouldn't use decibels. The final units should be sec/m since it is the inverse of speed. So the attenuation coefficient should have units of 1/(m-s^2) I think.