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I want to power some speakers via batteries. I have an old set of Boston Acoustics satellites that sound great. A pair of 2in satallites and a ported subwoofer around 4 inches. The sub is smaller than a shoebox.

The battery store near me sells sealed lead acid 12 volt batteries. They have one rated at 6 amp hours for $20. Good price if it works.

How do I know if the battery is sufficient to run the pseakers for 3-4 hours? The closet I can get to a power rating is when I look on the wallwart AC adapter is says "1500mA." If that means that the speaker draw 1.5 amps, then a 6aH battery will be good for 4 hours. That would work.

But is that true? Does 1500mA on the wallwart mean that the system draws 1.5 amps? Is there some other spec I need to know about?

Power supplies PROVIDE power. Devices DRAW power. What is the power requirement of the speakers? It should be on the speakers. I would call Boston Acoustics and see what they say your quirements are. You may have to have more than 1 set for longer gigs.

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>>>..What is the power requirement of the speakers?...>>>

That is what I don't know. Its not printed on the label or anything.

Let's see if I can explain this.
The AH rating of a battery is based on a 20 hour test. How many amps can it draw continuously so that at the end of 20 hours the battery is at 10.2 volts DC.
An example:
If a battery is rated at 200 AH that means it was capable of a 10Amp draw for 20 hours before reaching 10.2 VDC.
The issue here is that just because a 200AH battery can draw 10 Amps for 20 hours doesn't mean it can draw 200 Amps for one hour. So 6AH is not much here. 6/20= .3 Amps. That Batt will handle .3 amps for 20 hrs before it reaches 10.2 VDC. So how many amps will it handle for 4 hrs? Look at the chart for the battery. The other key here if you picked up on it is 10.2 VDC. This is way lower then then usable voltage of most electronics. This is what really skews the AH rating of batteries.
BTW I was the head of the electronics Dept. for the biggest yacht builder in the country. Big Sail boats. Lots of batteries

BTW if your speakers draw 1.5 Amps @ 120VAC that translates to 15 Amps @ 12VDC

The power supply rating of 1500mA is the maximum current it can safely provide. It does not mean the speakers actually require that much power. However, it's a reasonable bet they require more than one amp, or they would have supplied a cheaper walwart rated for 1000mA or so.