A broadband wavelet approach to ultrasonic pulse-echo time-of-flight measurements is described. The broadband approach significantly reduces the time required for frequency-dependent pulse-echo measurements, enabling studies of dynamic systems ranging from biological systems to solid-state phase transitions. The described broadband approach is demonstrated in parallel with the more traditional frequency stepping approach to perform ultrasound time-of-flight measurements inside a large volume Paris-Edinburgh press in situ at a synchrotron source. The broadband wavelet data acquisition process was found to be 1-2 orders of magnitude faster than the stepped-frequency approach, with no compromise on data quality or determined results.