How Do You Calculate the Loudness Factor (\cal F) for Different Frequencies?

[roldy]

Homework Statement

Determine the loudness level and loudness of a 100 Hz tone with an intensity level of 60 dB ref. 10^{-12 } W/m^2.

Homework Equations

Loudness=N=0.046\times10^{L_N/30}
Loudness Level=L_N=L_I+30log{\cal F}

The Attempt at a Solution

I would be able to solve this problem if I only new how to obtain \cal F. My book says that it is an empirically determine parameter depending only on frequency. I've tried looking in the book but it is of no help. What does \cal F mean and how do I obtain it?

 

[diazona]

Hmm... well, I can't say for sure without more information about the exact meanings of the variables in your formulas, but I suspect that \mathcal{F} might be some sort of weighting function. Basically it's a term that compensates for the fact that the human ear perceives sound waves of the same intensity at different frequencies as having different volumes.

 

[roldy]

I forgot to mention that L_I is the intensity level.