Can I use a transformer with center tap to convert 240V to 120v?
what you have drawn would work if sized correctly based on voltage.
 However the U.S. power is 60HZ,  I thought you were on 50HZ. The lower frequency may cause issues with the amplifier filter circuits (audible hum or buzz)
I would look into that first , then think about a “step down” transformer 2:1 .
The reason I would point you in that direction is the center tapped system would need at a bare minimum 2X the wattage. 
I usually over size transformers by 50% (wattage) to reduce the heat created and extend the transformer life. 
The power your unit requires to run is the important thing not the amplification wattage if it is a 500w amp it will take far more run the system than 500W.