Apparatus for determining a thickness of a wall of a pipe, featuring a signal processing module configured to respond to signaling containing information about traveling stress waves transmitted to and reflected back from a wall of a pipe by a sensor band that includes a series, ring or array having multiple transducers circumferentially arranged and mounted around, and attached to or clamped onto, an outside wall of the pipe; and determine a profile of a thickness of the wall of the pipe corresponding to circumferential locations of the multiple transducers based on the signaling received from the sensor band; and one or more orientation or rotation sensors, each responding to its orientation in relation to its displacement on the pipe and to provide an orientation signal containing information about the same.