You do not need to get under the car to do most of the investigation work. The exhaust manifold comes out in front of the engine. The exhaust pipe connects to this, and then runs under the engine and car. The front of the exhaust manifold system is shielded with thin metal plates.
The manifold can leak at the joints or sensors going into the system. There is an exhaust pipe flex link under the car, right about where the front seats are. This link is a very common point of exhaust leakage. It looks like a pipe made out of wire. The other less common location is where the exhaust pipe bolts to the manifold system. The manifold system incorporates a catalytic converter in addition to running to each cylinder.
It may be possible there is problem with the air intake system, such as the filter box. The air intake system is designed to muffle the noise of the air going into the engine. Since the noise seems only to accrue when accelerating, it may be a problem in this air intake system. As the car runs OK, the problem must be before the throttle body. This is the part on the intake system where the throttle cable attaches to a pulley.
Pipe up a length of rubber hose to use a stethoscope and help run down the exact leak location. If an exhaust leak, you may be able to feel the exhaust coming out of the leak. Of course be careful, as the system is very hot.
Download the service manual for this Generation of Camry (Gen 3) engine from the link below:
http://oregonstate.edu/~tongt/camry
This will give you an idea of the engine system design. Where the joints are in the exhaust system, air intake system, etc.
Once you do this, you have a better idea where to look for the leaks.
Strange sound at the tiime of accelearation
strange sound
Linear Mode
