Check the voltage right at the amp when the speakers sound bad. If the amp isn't getting sufficient voltage then it will not sound right.
If the volt meter on the dash isn't reading at least 13 volts then your alternator is not providing enough current. Adding a second battery will only extend (by an hour or so) the time before you are dead. If you are not producing what you consume, you need to either consume less or produce more.
Before you jump to that conclusion, however, can you expand on your statement? If the engine isn't running and you are getting 12 volts then there isn't a problem at all. Before you apply what I said in the paragraph above see what the guage reads after you have been running at cruising speeds for at least 5 minutes.