We present theoretical solutions, based on linear acoustic theory, for axial acoustic particle velocity in an annular region of a coaxial duct. The solutions are expressed in terms of two non-dimensional parameters h/δ(ν) and R; h and δ(ν), respectively, represent the half of the spacing between two concentric ducts and the characteristic length given by kinematic viscosity of the gas and angular frequency of acoustic oscillations, and R is the radius ratio of the ducts. The validity of the solutions was verified by direct measurements using a laser Doppler velocimeter. The present results are applied to measurements of the acoustic power distribution in a traveling wave thermoacoustic engine with a coaxial duct, which provides experimental evidence for acoustic power feedback in the coaxial duct.