Quoted from [this](https://dsp.stackexchange.com/questions/1823/how-do-phons-relate-to-loudness) 

> 
> As a first order approximation it takes ten times the energy to double the perceived loudness
> 
> 
> 

So is there a 2nd order approximation. If so then how much change in RMS value doubles perceived loudness? Is it governed by any system of equations?

Thanks