How to figure out battery life of audio amplifier?
Taking a standard capacity number for AA (Alkaline, good brand) of 2500mAh, and a conservative average draw of 1 Amp for the amplifier (which is a fairly large draw on AA batteries). Since the Chip has a max VIn of 5.5V, you will be powering with 2 AA in Series, In Parallel, giving 3V and 5000mAh.


  It drives up to 2.7 W (10% THD+N) into a 4 Ω speaker. With 85% typical efficiency, the TPA2013D1 helps extend battery life when playing audio.


So given a 4Ω speaker at max, you get 87% efficiency, so the capacity is more like 4350mAh. With a lower operating voltage, that's more like 83 to 80% based on the graphs.

A off the cuff napkin calculation of 4300mAh / 1000mA = 4.3 Hours. Round down for voltage drop and loud songs, I figured on 4 hours max, with GOOD batteries, not cheapo ones.

Of course, max volume, speaker's resistance value, temperature, etc can affect that, but that is your top end without empirical testing, or going with beefier batteries (C, D, etc)

Also, its the "TPA2013D1", not "TPA2013D".