Frequency-domain travel time (FDTT) measurement of ultrasonic waves by use of linear and nonlinear sources

This paper describes a frequency-domain travel time (FDTT) method for measurement of direct and reflected travel times of sound waves based on the change in phase with frequency between a reference signal and a transmitted wave. An ordinary (linear) source can be used for measuring delays over shorter path lengths, and a parametric array (nonlinear) source can be used for measuring delays over longer path lengths. In the ordinary source measurement a reference signal is electronically multiplied with a signal that is time delayed by propagation through a sample. As frequency is incremented stepwise, the relative phase difference generates a corresponding stepwise dc output from the multiplier. For any travel path within the sample, there is a characteristic period of the dc signal whose reciprocal is proportional to the group time delay along the path. If more than one arrival exists, characteristic periods are superposed. An inverse Fourier transform of the frequency signal gives the discrete arrival times for each path. In the parametric measurement, a second electronic multiplier is used to create an electronic difference frequency signal for phase comparison with a wave at the difference frequency created by nonlinear elastic interaction in the material. The FDTT method should be applicable to ultrasonic investigation of material properties, nondestructive evaluation, seismology, sonar, and architectural acoustics.