It's a very simple circuit, but I wouldn't be that quiet. Transient periods will generate huge losses between both transistors of each driver.
The square wave goes from 0 to 12V (aprox.) in a very short period of time, when the signal will take every voltage value between these given two. Whenever it's higher than 0.7V and lower than 11.3V both transistors are switched on, so if by miracle they don't burn up, they will heat a lot and waste energy which is precious in this application (battery supplied).
I would use the opposite configuration instead, a NPN in the high side and a PNP in the low side, a simple voltage follower as each H-bridge driver. This will need an additional transistor to invert one driver's input so it's high when the another is low.
Proposed circuit. Sorry about lack of values for 555 oscillator but I don't have time to calculate them, you can use an online calculator. Keep in mind that Rc and Rd (charge and discharge resistors) shouldn't be higher than 100K. Always prefer keeping frequency beneath 60Hz because most phone chargers are designed to operate between 50-60Hz and not higher frequencies, so if in the calculator you get "57Hz" it's more than OK, even because of the components tolerance value (error) you could get 55 or 60Hz once the circuit is mounted in the PCB.
The transistors you're going to use are D'arlington arrays, such as TIP135 or TIP122 or that family, they are cheap and accesible.
I recommend you to mount it in a PCB since breadboard contacts are very poor for driving high currents.
Hope being helpful.