Vibration when accelerating hard at highway speeds

Recently purchased a 2004 S4 manual with 53K miles, on the way back from dealer, noticed a vibration when accelerating hard at highway speeds 60mph to 80mph roughly.  Now this is the first time owning a car with a V8, so not sure if it is just a combination of the age of the vehicle and/or the power from the engine.  It is not a violent vibration, but it can be felt through the steering wheel and I noticed the mirror slightly vibrating when changign lanes during acceleration.  One acceleration stops and just cruising, all vibration goes away.  Car feels great and extremely responsive otherwise.  Just inexperienced with this type of engine/car.  I do own a 2008 A6 3.2 and when pushed, there is no vibration at all, but there is also a difference of 100hp and 50tq. Again, this was under hard acceleration. Runs smooth when driven normally.