I have a 2000 Jaguar XJ8. What is causing an engine noise (sort of like a motorcycle) whenever I accelerate?

You have an exhaust leak, either in the exhaust system, or at the manifold. By your 'Harley' reference I would suspect the manifold. You might be lucky and just be able to replace the gasket, but the labor involved would not be cheap. But in all honesty, manifolds crack more often that manifold gaskets fail.