We consider a scalar 1-D linear hyperbolic partial differential equation (PDE) for which infinite dimensional backstepping controllers have previously been designed based on boundary actuation and sensing, and incorporate first order actuator and sensor dynamics into the design. Two observer designs are proposed, and combined with a state-feedback into output-feedback control laws which render the origin of the closed-loop system exponentially stable with arbitrary convergence rate. The theory is verified in simulations. (C) 2018 Elsevier Ltd. All rights reserved.