How to melt sand with microwaves? Is it possible to melt sand with microwaves? Which frequency should they have?
The melting point of the sand is 1.700°C and the mass is not homogeneous: there are a lot of pores and the composition of sand is not homogeneous.
 A: Yes, it is possible to melt sand with microwaves. However, you won't be able to do it with your household microwave. You will need something with a much higher field strength (and much more power).
The absorbed microwave energy P can be calculated by 
$$
P=2\pi f \varepsilon_0\varepsilon''_r\left|E\right|^2V
$$
Where $f$ is the frequency, $\varepsilon_0$ is the electric constant, $\varepsilon''_r$ is the so called "Loss factor", $E$ is the electric field intensity and $V$ the volume. 
Sand is mainly silicium dioxide which has a very low loss factor (see for example Westphal1972). (All the impurities in sand will increase the loss factor a little bit - depending on the impurities it might be a little bit more). Porosity makes it even worse.
However, once you pass a certain temperature level (about 500°C to 600°C) the absoption becomes much better.
While you heat the sand it will give off heat to the surrounding microwave cavity. The hotter the sand gets, the higher will be the losses (thermal radiation heat flux is proportional to $T^4$). So, you will need an insulation material that can withstand the temperatures and stays microwave transparent. In an inert atmosphere you could use boron nitride as container and radiation shield. Beyond the radiation shield you could put high alumina ceramic fibers (not ideal, but it works).
And thats it: Thats how you could melt sand with microwaves.
A: Microwave heating requires the presence of dipoles in the material to be heated. Sand consists mainly of quartz which does not contain dipoles. So microwaves are not suitable for melting sand.
You can e.g. use the focused light of a solar furnace to melt sand.
A: I think it is possible, in principle, to melt sand with microwaves, say, at a frequency used in microwave ovens (2.45 GHz). I agree that dry silica sand does not absorb much at this frequency, but it does absorb a small part of microwave power (http://www.jmpee.org/jmpee_site/Vol_47(3)/JMPEE47-3-199Liu.pdf , Journal of Microwave Power and Electromagnetic Energy, 47 (3), 2013, pp. 199-209). Perhaps you need a more powerful microwave source than an ordinary microwave oven, so that the absorbed power exceeds the losses.
There is another possibility. If the microwave source is powerful enough, it will cause microwave discharge in the sand (for this you need electric field of microwave radiation of the order of 10 MV/m), the sand will become conductive and will absorb microwave power.
A: Fire is hot. Hot gasses given off light. If they are very hot, most of the light is of a wavelength we can see. Cooler objects objects give off longer wavelength light that we cannot see. Typically this is mostly in the infrared part of the spectrum. Really cold objects glow mostly in the very long microwave region. For all such objects there is quite a spread of wavelengths. And hotter object give off more light than colder objects.
Light carries energy. When light strikes another object, it can be absorbed. The amount of absorption depends on the wavelength and the type of material. Absorbing energy makes the object warmer. 
A really hot fire can melt glass through radiation. This is how glass is melted in furnaces. 
This post explains how it happens, and what regions of the spectrum do what. Why does glass absorb infrared light?
A: Microwaves correspond to the radiation which would cause molecules in a gas or liquid to rotate. In sand, which is typically quartz ($\text{SiO}_2$ ), the "molecules" are locked into place and can't rotate. Thus using microwaves to melt sand would be impossible. 
