Is there any relationship between electrical impedance and wave impedance? I'm a student studying EM right now and the concept of wave impedance has come up. I think I understand the mathematical derivation of it and I understand how to use it to calculate reflection and transmission coefficients. However the unit Ohm I think is confusing me.
In standard electrical circuits the electrical impedance is related to the power dissipated. There is a voltage drop across and a current through the impedance. In purely capacitive or inductive loads there is simply a phase shift (in AC). This stuff is mostly intuitive to me as I can kind of imagine 'electrical energy' moving through a circuit and how it interacts with these components.
Wave impedance seems to me, to be a measure of an intrinsic material property, there is no power dissipated. In my limited time with this topic it seems to me that it doesn't have much real/physical meaning except at the boundaries of materials. This is doing my head in, the same unit seems to be being used for two seemingly unrelated things, more than that, the same word 'impedance' is being used.
Is there some relation between electrical and wave impedances that I've misunderstood? Is there a more intuitive way to wrap my head around wave impedances (some analogy maybe)?
Or will I need to come to terms with $\eta$ being a useful number derived from
Maxwell's equations that simply exists.
 A: There are several "impedances". In general, we can say that it relates an input with an output for a particular system of interest. Some of them are "intrinsic" and some are "extrinsic".
Extrinsic


*

*Acoustic impedance, that relates pressure with volume flow rate.

*Electrical impedance: relates voltage with current.

*Mechanical impedance, that relates force to velocity.
Intrinsic
These are properties of each medium.


*

*Elastic impedance: relates stress with velocity. It is given by $\rho c$, where $\rho$ is the density and $c$ is the phase speed of one of the waves in the medium.

*Characteristic acoustic impedance: relates the pressure with particle velocity. It is given by $\rho c$, where $\rho$ is the density and $c$ is the speed of sound.

*Wave impedance: relates electric and magnetic fields. Given by $\mu c$, where $\mu$ is the permeability of the medium and $c$ the speed of light in this medium.
A: you can check this two links https://en.wikipedia.org/wiki/Wave_impedance & https://en.wikipedia.org/wiki/Electrical_impedance 
as they mention in the former that the symbol η (eta) may be used instead of Z for wave impedance to avoid confusion with electrical impedance.
A: In EE we say circuits are impedance matched meaning there is maximum energy transfer. Example is 50 ohm coax cable to transmit signals minimizing reflections to the final resistance load (50 ohm) or impedance load like an antenna. So the ohm term is used both for resistive and reactive-inductive loads.  Inputs of most oscilloscopes and outputs of many signal generators are 50 ohm, both impedances guaranteed to a certain frequency range for performance, it's a standard (as is 75 ohm). An inductor has an impedance of j ω L given in ohms, note that the ohms are frequency dependent with L. In the right circuit this 50 ohm inductor impedance could be matched to a 50 ohm resistive load to maximize energy transfer.  Impedance matching is an important concept in all electronics: radio, circuit board traces (especially high frequency) and to antennas ( the atmosphere has a 377 ohm impedance which we must match to).
