Echo and Source Boundary Depth Scans

Echo Launch-Time Three-Row Scan

The echo arrival is launch time plus twice the one-way delay, so shifting the launch shifts the echo by the same amount with the line delay fixed. On a 12 m line at 3 m/s the one-way delay is 4 s, so launch times of 0, 2, and 5 s give echo arrivals of 8, 10, and 13 s exactly for the ideal lossless-line model; real lines add attenuation, dispersion, finite rise time, impedance tolerance, source and load mismatch, cable losses, connector parasitics, and timing and voltage measurement uncertainty.

Echo arrival is scanned by changing only launch time. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Echo arrival shifts with launch time

The line delay is fixed here. Moving the launch later moves the return later by the same amount.

techo=tlaunch+2tone=0 s+8 s=8 st_{\text{echo}}=t_{\text{launch}}+2t_{\text{one}}=0\ \text{s}+8\ \text{s}=8\ \text{s}
Launch-time echo scanThe one-way delay is fixed; only launch time changes.outecholaunch 0 sone way 4 sround trip 8 secho 8 s

Echo arrival shifts with launch time

The line delay is fixed here. Moving the launch later moves the return later by the same amount.

techo=tlaunch+2tone=2 s+8 s=10 st_{\text{echo}}=t_{\text{launch}}+2t_{\text{one}}=2\ \text{s}+8\ \text{s}=10\ \text{s}
Launch-time echo scanThe one-way delay is fixed; only launch time changes.outecholaunch 2 sone way 4 sround trip 8 secho 10 s

Echo arrival shifts with launch time

The line delay is fixed here. Moving the launch later moves the return later by the same amount.

techo=tlaunch+2tone=5 s+8 s=13 st_{\text{echo}}=t_{\text{launch}}+2t_{\text{one}}=5\ \text{s}+8\ \text{s}=13\ \text{s}
Launch-time echo scanThe one-way delay is fixed; only launch time changes.outecholaunch 5 sone way 4 sround trip 8 secho 13 s