If your playing with map contacts on - then if you select and enemy escort you will see some rings around him. The largest - a ring - appears to be passive sonar detection range. The farther in you are - the better chance he has of hearing ya. Of course - keeping the noise to a minimum helps - set silent running and go no faster than 2 knots. Do that and you can avoid him unless he gets REALLY close.
The little half circle in front of the DD is his sonar cone - get within it and he will likely be pinging at you. At that point - your pretty much found.
On occasion - I have seen 2 large rings - the very large one then appears to be visual range, the interior one being passive sonar range, and the half ring still being active sonar.
And yes - the Ping sound you hear is active sonar....
As for detection range - there is no "set" number. It all depends on a number of factors. How much scope do you have above the water - higher out of the water is bad. A couple of feet is likely the most you want out. I tend to use the pgup and pgdn keys until I stop getting water on the lens and stop there. The next factor is sea state and air state. In fog, or a storm, your MUCH less likely to be spotted. Next is how fast your going - faster means more noise as I mentioned above - but also makes your scope (or you on the surface) more visible. So slow is good. The last main variable is enemy skill level. An elite crew doesnt have to see you - they can SMELL you even if your downwind. (Dont take this personally - they do it to us all - its NOT just you.
). The least skilled crews - man you could pull up, tie alongside em and board them and they wouldn't notice. So this one factors in alot.
Since I use manual targeting - I always go for the really close shots. If you keep the scope down as much as possible, go slow (use silent running!!!) and position yourself where the target comes to you - then you can get within 500 yards/meters on a regular occasion without getting spotted.