The dependence of the measured damping rate upon the neutral beam heating power (P-NBI) and plasma beta has been experimentally investigated for n = 1 toroidal Alfven eigenmodes (TAEs) in JET limiter plasmas with a monotonic safety factor profile and low edge magnetic shear. The mode frequency is observed to decrease with increasing beta, as predicted by various theoretical models. For low P-NBI < 3 MW, a single n = 1 TAE splits into two modes closely spaced around the expected TAE frequency, and the mode damping rate decreases with increasing beta. On the other hand, at higher P-NBI > 6 MW, no frequency splitting is observed and there are indications that the mode damping rate increases with increasing beta.