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.