Stationary waves and transfer of energy I have seen a question posted similar to this, but I am not sure if it answers what I was wondering about.
Essentially, we are taught that there is no average energy transfer of a wave to its surroundings. I understand that it intuitive for a mehanical wave on a rope, or even an electron that is bound to an atom. However, stationary waves can also form in microwaves, which are responsible for heating up food. This is also fairly obvious, as the electric and magnetic fields interact with the dipoles of the water molecules. 
However, there is a contradiction, and I am not sure exactly where my misunderstanding is. Could someone point it out? Thanks!
 A: In a empty microwave oven, you create standing wave. And if it's empty, there is no transfer of energy to anything.
Now let's say you put a glass of water right in the middle of your MW oven, The molecules of the water (H20) have resonancies due to their internal structure : vibration, rotation etc...  When the frequency of the oven is one of those frequency, their is a transfert of energy from the standing wave to the liquid (heat for the liquid). 
That's why you should place you plate in the middle of the oven, that's where the electromagnetic field si the most import and it's the place where you can transfert the more enrgy from the standing wave to you plate. And of course, the oven supply more power to keep the standing wave at about the same amplitude. But you need to inject power into your standing wave
A: Answer
An analogy may help here...
Think of two people A and B with a jump-rope on a playground wiggling it up and down, creating waves. Since the two people at the ends act as fixed points for the rope. The wave moving from A to B (for example) will be reflected off of person B, and a standing wave forms.  Now the energy of the wave simply sloshes back and forth between the two people.
So currently, we just have a system where energy is "trapped" between two points, and doesn't go anywhere, because the wave isn't going anywhere - this is a key feature of a "standing wave", and indeed this is precisely what's happening inside a microwave - the waves bounce off the walls, and slosh back and forth inside the container.
Now imagine a third person, C, decides it's a good idea to lie between A and B and therefore underneath the wiggling rope.  Now person C will be repeatedly hit by the rope, and in this way, some energy is transferred to her.  Note that this isn't due to the waves moving directly to her, rather she is in the way of the oscillations of the waves, and now the standing wave is not "pure".
In the microwave, water molecules in food / drinks get "in the way" of the microwaves, and "get hit" by the electromagnetic oscillations (I use inverted commas, because of course microwaves aren't physically hitting the molecules).  In this way, the water molecules absorb some energy, and heat up as a result.  Again, it's not that the microwaves are travelling directly to the water molecules and delivering their energy this way, rather the water molecules are taking advantage of the oscillating field that's otherwise just sitting in the microwave, not going anywhere else.

Yummy experiment
Not sure if you've ever seen this, but if you remove the turn-table in the microwave, place a bar of chocolate in the middle and let the microwave run for a bit, you should find that there are regions which are melted, and regions which are uncooked.
The melted regions are those where the standing wave has "hit" the chocolate bar (position of antinodes) whilst the untouched parts are the positions where the standing wave amplitude was zero (nodes) and thus no oscillating field was present here to allow the water molecules to resonate.
From this, you can also deduce the wavelength of the microwaves in your machine, and if you know its frequency (perhaps quoted on the machine somewhere), you can find the speed of light!
And after all that hard work, you can reward yourself with some semi-melted chocolate (just be sure to clean the microwave...)
