# how to convert decay time to power law coefficiants

In audio, I am familiar with the definition of t-60, which is a characterization of a room impulse response (RIR) decay time. This characterization demands that the sound will have a 60 db decay over the specified time.

I am now trying to define a medium in a given tool that requires this decay to be evaluated using the power-law $$\alpha = \alpha_0f^y$$ and I have to define $$\alpha_0$$ and $$y$$.

How do I convert a specific decay time $$t$$ to the correct $$\alpha_0$$ and $$y$$, specifically in air and generally in another known medium?

• What would be the value of $f$? Also, is $t$ supposed to be the $t_{60}$? – A_A Oct 15 '20 at 14:51
• $f$ is a given frequency (decay is a function of the frequency). $t$ it the decay time, so, yes, $t_{60}$. – havakok Oct 16 '20 at 11:10
• Correct me if I am wrong but I believe that the decay in a room is not a function of only the medium. Boundary conditions (i.e. material with specific impedances), as well as geometry, play an important role in the determination of the decay time. Thus, I am not sure this can neither be described with two constants deduced from specified medium characteristics nor it can be calculated without knowledge of the aforementioned quantities (boundary conditions, that is). Unless of course, you want to work statistically, which will eventually end up somewhere close to Sabin's equations family. – ZaellixA Oct 20 '20 at 11:08