1963 Other Chevrolet Models sporadic rattle noise

i have a '63 chevy biscayne 6 cyl / 235 / 3 speed....recently i have inherited a sporadic rattling noise when i accelerate...then as the car moves faster it fades.....it almost sounds like a wiggling noise to me directly under the engine. my mechanic suspects that muffler/tail pipe/brackets need to be replaced-appears to be the original. other than for a small oil leak when the car is turned off... it rides good.
this problem just started up...the rear wheel bearings were replaced recently...and having owned it over the past year have made several other repairs so the car can be used as an everyrday ride.
any suggestions??? thoughts???
thank you.
william allegar