Frequency-domain reflectance for six uniform tubes of different lengths. The reflectance magnitudes all have values close to 0 dB for frequencies less that 1 kHz. The group delays are relatively constant between 0.1 and 10 kHz, with the shortest tube having the smallest group delay. Outside this frequency range, the group delay displays some oscillation.
Time-domain reflectance (TDR) for six uniform tubes of different lengths. The peak value of TDR is between 0.26 and 0.27. The latency of the peak corresponds to the round-trip delay for the sound waves to propagate from the measurement probe to the closed end of the tube and back to the probe. This latency is an orderly function of the length of the tube, with the largest latency for the longest tube, and the smallest latency for the shortest tube. The circle denote the reflection round-trip delay.
Uniform tube diameter inverse solution (solid lines) obtained from the time-domain reflectances. The dashed lines show the true diameter functions for comparison. Except for the gradual decrease in the diameter function at the end of the tube, the inverse-solution can determine the diameter functions and the lengths of the acoustic tubes. The length of the tube here is the actual length of the tube minus the probe insertion depth and was determined from the round-trip propagation delay of the sound wave. The circle denote the reflection distance
Communication Engineering Laboratory