The tomography data were used to determine the signal velocity along the longitudinal direction of the PV staves. Scatter plots were made of the distance from the left side of the stave as measured by the wire chamber versus the timing of the signal. Two of these plots can be seen in Figure 4.7. The slope for these plots was extracted from each of the scatter plot intensity enhancements.
The average speed determined was (7.7 ± 1.0) × 107 m/s or about 24.5% the speed of light in vacuum. This indicates that if a TDC with a 0.25 ns resolution is used, the position along the stave through which the particle passed can be determined to within ~ 2 cm. The BC-400 material from which PV staves were constructed has a refractive index of 1.58 making the speed of light only 63.3% of that in vacuum. The additional reduction in the speed of the signal is due the indirect path taken by the light signal from its point of origin to the PMT (i.e. the light undergoes many reflections in the stave). The signal velocity is thus about 2.6 times slower than the speed of light in BC-400. The signals, on average, can be considered as having traveled through about 2.6 times as much material as they would have if the signal were to travel straight down the stave without any reflections. This is roughly consistent with the factor of 4 discrepancy between effective attenuation length of the staves and the nominal attenuation length for BC-400 material. The remainder of the discrepancy is due mostly to reflection inefficiencies