To test whether either or both O2 sensors are damaged, one hooks the (black, following Bosch's convention) wire on each sensor and tracks the signal against the ground using an oscilloscope.
When the car is idling at 3000rpm, the upstream sensor will show a wave with an amplitude in the range between 0.2 V and 0.8 V, and a frequency between 1 Hz and 2 Hz.
The signal looks like this:
The downstream sensor should have a much more constant signal. This stable signal indicates that the catalytic converter is doing its job and there is no fluctuation in the level of O2, or not as much, past the cat.
How can an engine revving at 3000 rpm produce a variation in O2 of frequency 1-2 Hz rather than 50 Hz? I'd have been surprised if the O2 variation was anywhere near 3000 Hz; there surely must be enough turbulence in the engine outflow for any variation to vanish, but I'm still surprised that there is a variation at this low frequency. What causes it?