The alternative to frequency domain measurement is to measure the time domain response, for instance, by acoustic pulse reflectometry. The history of this technique has been reviewed in detail in the thesis of Sharp [6]. A summary is presented here.
Acoustic pulse reflectometry was at first developed as a technique for the study of the earth's crust, especially for oil exploration. Generating an explosion at the surface causes an impulsive acoustic wave to travel down into the earth. A proportion of the incident wave is reflected when a change in density occurs within the rocks. In general there will be many layers of different density within the rocks in the earth's crust resulting in a complicated response which can be measured at the surface. Ware and Aki [7] were the first to provide an algorithm for calculating the densities of the layers from this impulse response. Their method assumed no acoustic energy was lost to heat during propagation.
Applying the same technique to propagation in air means producing an airborne pulse, for instance using a loudspeaker or spark discharge. Reflections of sound within tubular acoustic structures then arise at changes of cross-sectional area. This was first suggested by Sondhi et al. as a way of determining the internal area profile of the mouth cavity [8,9]. Experiments were performed on vocal tracts and lungs by Jackson et al. [10,11]. A spark was used as a sound source, with the resulting pulse travelling along a section of cylindrical tubing called a source tube, then into the airway under test. The resulting reflections were measured by a microphone in the source tube wall. The reason for the source tube was to physically separate the in-going pulse signal from the impulse response. Measurements on human patients were performed by Fredberg et al. [12] and clinical use followed [13].
The first attempt at using pulse reflectometry on musical wind instruments was made by Benade and Smith [14]. While the lack of losses in the Ware-Aki algorithm posed no problem for the measurement of human airways, the longer length of many musical instruments means that losses play an important role in the impulse response and need to be included for an area profile algorithm to provide accurate results. Further work was performed by Smith [15]. Watson and Bowsher found that a reasonable reconstruction could be found by changing the dc offset in the experimental measurement untill the algorithm predicted the desired value of the bore radius at the open end [16]. This method of finding the bore is not always accurate since losses are not included explicitly. The effect of losses and dc offset are qualitatively similar meaning that the lack of losses may be loosely compensated for by a false dc offset value. An alternative algorithm was developed by Amir et al. which incorporated viscothermal losses [17,18]. This was used by Sharp et al. to provide accurate reconstructions of the internal profile of brass instruments [6,19,20].
While the main motivation for development of time domain measurement was to perform the calculation of the area profile from the measured response, the input impedance can also be deduced from the impulse response. The experiments presented in this thesis were performed using acoustic pulse reflectometry. Chapter 5 describes the existing setup for the measurement of musical wind instruments and we then go on to discuss practical improvements to the technique in chapter 7.