# Measurements in finite-length uniform tubes

### Frequency-domian reflectance

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-domian reflectance

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.

### Area function

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

audres.org

Boys
Town
National
Research Hospital

Communication Engineering Laboratory

Last modified: 12-Aug-11 daniel.rasetshwane@boystown.org