How the fade is applied
This tool runs FFmpeg's afade filter twice, once at the start of the file for the fade-in and once near the end for the fade-out, each ramping the volume between silence and full level over the length you set, from 0 to 15 seconds. The fade-out's start point is calculated automatically from the file's total duration, so a 4-second fade-out on a two-minute track always lands exactly at the last four seconds, with no need to work out the timing yourself.
The curve you choose controls the shape of that ramp, not its length. Linear moves the volume at a constant rate across the whole fade, which is simple but can sound slightly abrupt, especially near the end of a fade-out where a constant rate suddenly meets silence. Logarithmic, exponential and quarter sine curves instead change more slowly at the start and more quickly near the end, which tracks how human hearing perceives loudness changes and tends to sound smoother and less noticeable as a fade.