Some answers can be found in IEEE 802.3, however care is needed when reading that document, there were a lot of variants of Ethernet and if you aren't careful it's easy to end up reading the wrong section.
The electrical specifications for 10BASE-T can be found in 220.127.116.11.1
The peak differential voltage on the TD circuit when terminated with a 100 Ω resistive load shall be between
2.2 V and 2.8 V for all data sequences for a type 10BASE-T MAU that is not a type 10BASE-Te MAU.
For 100BASE-TX it appears that 802.3 does not directly specify PHY electrical characteristics, instead clause 25.2 references another standard.
The 100BASE-TX PMD (and MDI) is specified by incorporating the FDDI TP-PMD standard, ANSI
INCITS 263-1995 (TP-PMD), by reference, with the modifications noted below. This standard provides
support for Category 5 twisted pair cabling. For improved legibility in this clause, ANSI INCITS 263-1995
(TP-PMD), will henceforth be referred to as TP-PMD.
Unfortunately that standard doesn't seem to be freely available and I'm not paying $60 to answer a stack exchange question.
Looking at the section on 1000BASE-T i'm struggling to find a clear statement of output voltage, but Figure Figure 40–20 shows a scope trace with a signal varying up to around ±1.5V when transmitting a test waveform.
10BASE-2 and 10BASE-5 are specified in terms of current drive instead of voltages. e.g From clause 10.4.1.3 for 10BASE-2
the signal has an offset com-
ponent (average dc current including the effects of timing distortion) of from –37 mA min to –45 mA max
and an ac component from ± 28 mA up to the offset value.
So potentially you could have an offset of –45 mA and an AC current of ±45ma leading to a total max current of -90 mA. This drives into a 25 ohm load, so that works out to a maximum of around -2.5V, into a properly terminated cable. However the voltages may be higher if multiple stations transmit at the same time.
Either way though, your professors mentions of 9V and 12V do not seem to be in any way reflective of reality.