Triumph Repair: noise from rear of car, air shocks, sound travels

Question
I have a 1980 Spitfire..

There is a noise that seems to be originating from the right rear, but being how sound travels I imagine it could be coming from anywhere in the middle to rear area. The best I can explain it is a hitting noise, as if some one was under the car and banged it sharply with a hammer. It happens just as the clutch is engaging, as you start to back up.It occurs as soon as the drive-train applies torque to the rear.  The car does not even necessarily need to move before the sounds occurs. The faster you let the clutch out the louder the pounding sound. It only makes the noise once before the car starts moving. It does not do it letting the clutch out going forward. It also makes the noise when going over bumps on the road, but it does not do it on all bumps. It is especially loud when going over railroad tracks.

It has all delron suspension bushings, a new leaf spring. and air shocks in the rear. It was all done less than 500 miles ago. It does not matter if there is 20 or 150 PSI in the air shocks.For those 500 miles I heard no hitting noise, until I took it out the first time this spring.

I tore the bolts out of the suspension on the right side yesterday thinking it may be caused by a cracked suspension bushing, but they all APPEAR to be OK. Everything appears to be normal. The driveshafts U-joints were recently replaced, but the rear U-joints (between the differential & hub) have not been replaced, but seem to be tight.

Is it possible that the shock is broken internally, or that a rubber bushing is cracked somewhere, but I can't see it. I way also thinking maybe something in the drive-train itself was causing it, but I do not understand why bumps, or going over railroad tracks would cause the noise if that were the case.

I am totally baffled, and desperate for an answer.
If you have ANY suggestions it would be greatly appreciated.

Answer
Hi Ed,
Noises are sometimes difficult to pin point. You may try putting the car on a lift and run the car in gear with the rear wheels suspended while you use a mechanic's stethoscope to try to locate the noise. Another method is to note if the noise is different in large right hand circles or left hand circles or straight ahead. A "U" joint can make noise even when they look good. The wheel bearings on a Spitfire are large needle bearings that run on the axle itself and difficult to access. You did not say if the car was disk wheel or wire wheel. The splines in a wire wheel can make the noises you talk about. A differential can also make such noises.
Your symptoms only tell you there is a noise and do not tell you what the noise is.
Howard