Bad exhaust sound but no bad exhaust!

[xexman44]

2007 Yaris, for no reason that I can tell, you hear a sound like the exhaust just ripped open. Your sure there is a hole or a seem that came apart but there is nothing wrong with the whole exhaust system. When you start the car it runs and sounds perfect. Then all of a sudden you hear the noise. I thought it would be an EGR problem but no EGR system on the car.
Even when the noise is happening and your standing there looking over the engine, you can't find anything wrong. Been a mechanic for a long time, no genius but this has be baffled. Any thoughts or ideas? 62,000 miles on the car. Runs perfect otherwise. Even runs good while it is making the noise. Like taking a kid to a doctor, when you try to work on it, it works perfectly.
Appreciate any thoughts. Thanks guys.
Joe B