From the beginning to the middle of WWII depth charges had a depth detonator set by the crew in advance. Only later with magnetic detonators and acoustic and magnetic homing depth charges (small torpedoes) and also the massive area bombarding by for instance hedgehogs depth changes for U boats helped less and less. Also combined with better detection equipment on the destroyers and radar on a bandwith narrow enough to see a raised periscope.
Under the history section of this Wiki page you will find a lot of answers.
https://en.m.wikipedia.org/wiki/Depth_charge
Best,
Ashi.