Methods of detecting pipeline weakening are described herein. The methods include creating a pressure wave in a fluid flowing in a pipeline using an input transducer located at a first position along the pipeline; measuring the pressure wave using an output transducer positioned at a second position along the pipeline that is spaced from the first position, and generating an output signal based on the pressure wave; analyzing the output signal to determine a stiffness of a sidewall of the pipeline positioned between the input transducer and output transducer; and determining if the sidewall includes a defect based on the stiffness of the sidewall, including analyzing a frequency response of the output signal to detect the defect.