I am currently using Windows 7 and I have installed Audacity from the exe.
I have just started using audacity, so my question could be inappropriate. I would like to create a sound that increases of 15dB from 55 to 70dB. In the Adjustable fade I set the FadeType on “fade up”, the Start (or end) on 55dB and End (or start) on 70dB and the handy presets on “Linear In”. then I genereate a simple constant sound with audacity and I regulate the volume of my speakers at 55dB. when I play the fading sound previously prepared, it starts at a lower intensity than 55dB and does not reach 70dB.
Moreover, if in the Adjustable fade I set the Start/End as in % of the original and I ask to generate a sound increasing from the 100% of the original to the 115%, still the new sound starts very low.

There’s a couple of things here.

Firstly, when dealing with signals, full track height (the maximum “valid” signal) is 0dB. All other valid signals are less than this - in other words, signals are measured a “minus dB”. A full scale signal is 0dB (peak level = 0 dB). A signal that is half the track height has a peak level of -6 dB (minus six). A signal that is a quarter of the track height has a level of -12 dB (minus twelve). Each halving of the track height is (approximately) -6 dB, so a signal of -56 dB is half the height of a signal at -50 dB.

-50dB is a very low level - it will look like a flat line (silence).
Working with the idea of half amplitude being -6 dB, then -48 dB is -6, -6, -6, -6, -6, -6, -6, -6 so that it 1/256th of the track height or about 0.004 of the track height. -50 dB is just a bit smaller than that.

dB measurements are always relative to something. “dB” is a “ratio”.
Normally when we talk about waveforms (signals) we describe the level with reference to 0 dB (the full height of the track).
We can also refer to the height of waveforms with reference to another waveform, in which case, if a waveform is twice as big as another waveform, then it is 6dB greater than the other waveform. If we amplify a signal “by” (say) 10 dB, then the amplified signal will be 10 dB more than it was before (about 3.16 times higher). This amplified signal will probably not be “10 dB” - the actual level (with reference to 0 dB) depends on how big the waveform was originally.

The other thing is that “Adjustable fade” is an “effect”, and like all effects it needs to be applied to some audio, so…
An example:
To create a sine wave that rises from -8 dB to -4 dB (note that -4 dB is closer to 0 than -8 dB and is therefore louder/higher amplitude).
First we would generate a tone at 0 dB (0 dB is the same as 1.0 on the linear scale), so use “Generate > Tone” and set the Amplitude to 1.0.