Hi hktk,
I’m not sure that I understand you question, but if I do then my answer may make sense!
When you drive a transformer at any frequency it will move around (physically) because of the forces that act upon it. These forces are produced by the magnetic fields interacting with the physical materials they meet.
It is therefore undesirable to generate physical oscillations within the range of human hearing, simply because people will be able to hear them. Its often wise to drive the transformer outside the range of domestic animals hearing, which can take the frequency to 25 or even 32 KHz, but obviously you have to think about your switching losses too.
Lets say we set the frequency at 12 KHz, a frequency that old and young people will hear, and we change the amount of power going through the transformer.
The power going through the transformer obviously relates to the flux density within the transformer. The flux density within the transformer will dictate the amplitude of the audible noise leaving the transformer.
The threshold that you refer to is related to the loudness of the noise that you will hear coming from the transformer. i.e. if your below a certain threshold the noise wont be heard (its still there it’s just at a level that is so low it wont be heard)
So in summary:
The threshold is how loud a noise has to be before it will be heard.
I guess there will be a relationship between the flux density and the noise level, but this will also be determined by a number of physical parameters including the size/type of core you are using, the type of former you have, the air gap in the core, the ambient temperature you are running the transformer at, the frequency you run the transformer at, and the actual temperature of the transformer.
So it may not be a practical figure to attempt to calculate, rather it would be a characteristic of the transformer that you would measure once you have built it.
Has that been of any help to you ?
Kind Regards Engineer Bob