You really can't get smooth DC from AC socket without a voltage regulator chip. A cheap zoom wall wart probably doesn't have one. The absolute best way to see what is going on would be to look at the wall wart's output on an O-scope. But unless you live near a DeVry, or an ITT or some college/career center with an electronics lab that is unlikely to be a option. If you can't afford a battery I doubt you can get your hands on decent test equipment.
You really should not be burning up batteries. I go more than a year and I play about 4.5 hours a week. Most basses I know with active guts use the input jack as a switch. The battery is only powering the circuit while the cable is plugged in. You unplug when done right?
Check your input jack to see if there are two wires soldered to it or three. If there are only two then your circuit is on all the time. If there are three the circuit is only on while the jack is plugged in.
If the jack has only two wires soldered to it, get a stereo jack and use the two ground leads to switch off the battery when you unplug. This is how lots of high end builders do it. My Smith bass had that and so did MTD if I recall correctly. My Warwicks also did it. It's a ten dollar part tops.
On a side note,
Weird stuff happens when you hook up power wrong. One time I was taking some active pickups out of one bass and putting it in another. There were two batteries so I just assumed they should be put in series for an 18 volt supply. When I plugged in I heard a radio station coming out the amp. I swear! It turns out the two batteries were supposed to be wired to +9 and -9. Weird! I didn't listen long enough to figure out what station it was. I was afraid it would burst into flames or something.
You really should not be burning up batteries. I go more than a year and I play about 4.5 hours a week. Most basses I know with active guts use the input jack as a switch. The battery is only powering the circuit while the cable is plugged in. You unplug when done right?
Check your input jack to see if there are two wires soldered to it or three. If there are only two then your circuit is on all the time. If there are three the circuit is only on while the jack is plugged in.
If the jack has only two wires soldered to it, get a stereo jack and use the two ground leads to switch off the battery when you unplug. This is how lots of high end builders do it. My Smith bass had that and so did MTD if I recall correctly. My Warwicks also did it. It's a ten dollar part tops.
On a side note,
Weird stuff happens when you hook up power wrong. One time I was taking some active pickups out of one bass and putting it in another. There were two batteries so I just assumed they should be put in series for an 18 volt supply. When I plugged in I heard a radio station coming out the amp. I swear! It turns out the two batteries were supposed to be wired to +9 and -9. Weird! I didn't listen long enough to figure out what station it was. I was afraid it would burst into flames or something.