OK if you need help you are going to have to be a lot more specific. What op-amp are we talking about? Most do not have a positive and negitave output. What is the schematic of this amplifier?
How is it powered? How is the RF module powered?
Is their any power supply decoupling on you system? How is it physically layer out ( photo please ).
In general What you describe as a slowly decaying sound does not seem to be what you think it is because the time constants are just too long for that.