Hi,
I agree that using a small 9v battery is not a good idea. To get 9vac from a
9vdc source it has to be boosted as mentioned in the other posts, and the
average current after inefficiencies would be around 1.2 amps if you are lucky.
This would drain an 9v battery pretty fast, and might even cause a large
drop in voltage so the boost would have to be a higher percentage which
would cause a higher input current. For example, if the voltage drops to 7.5v
under load the battery drain would go up to at least 1.4 amps, probably even
higher like 1.5 amps. This would kill the little thing quite fast and that's a
good thing because the tiny 9v would get pretty darn hot.
Go with an AA battery pack or a Lead acid battery as mentioned in the other
post unless you only need 5 minutes of operation.
If you decide to stick with 9vdc to 9vac then use a pulse first positive
and then negative, where the pulse average has the same average as
the ac sine wave would have over 1/2 cycle. This means a positive
pulse quite shorter than 8.333ms, then at the next half cycle a negative
pulse the same width as the positive one, then repeat. A micro controller
would come in handy here.
If you want to get more sophisticated, go with a PWM sine pattern.
As someone else said, a MOSFET H bridge would be good here, while
bipolars would most likely mean another drop in efficiency and so more
load on the battery.