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.
[Physics] How to melt sand with microwaves
microwaves
Related Solutions
A microwave oven :
A microwave oven converts only part of its electrical input into microwave energy. An average consumer microwave oven consumes 1100 Watts of electricity in producing 700 W of microwave power, an efficiency of 64%
So within the cavity it is something like 700Watts
The Bluetooth specification targets power consumption of the device from a "hold" mode consuming 30 micro amps to the active transmitting range of 8-30 milliamps (or less than 1/10th of a watt).
100milliwatts top, from the link.
These numbers tell me
a) that the energy needed to cook a kilo of meat in 10 minutes or boil water in a cup in 1 minute is about 7000 times higher than the highest energy consumed by Bluetooth.
b)The microwave is a cavity resonator trapping the energy. Blue tooth is an antenna, radiating and necessarily following the 1/r^2 fall of intensity of radiated electromagnetic energy. At a distance from the ear(1cm) of even 20cm the impinging energy energy will fall 400 times. That is why people who are fastidious or overly scared, or who are always on their mobile use the "hands free" supplied with the instrument.
Your question is based on a misapprehension. The heating in microwave ovens is not a resonant process. See the answers to Does a domestic microwave work by emitting an electromagnetic wave at the same frequency as a OH bond in water? for a discussion of this.
But let's leave this aside, because there is some interesting physics in your question. Suppose there was something that created an energy difference between orientations of the water dipole. For example, suppose we apply an external electric field so that the dipole aligned with the field has a lower energy than the dipole aligned against it. We'll tweak the field so that the energy difference between the two alignments is equal to the energy $h\nu$ of the microwave radiation.
A dipole aligned with the field can absorb a photon and flip into anti-alignment. This is like hitting the bell i.e. it adds energy to the bell. However the radiation can also cause stimulated emission of the excited state so it decays to the ground state by emitting a photon - you'd put one photon in and get two out. This is like hitting the bell in antiphase - hitting the bell in antiphase means your hammer rebounds with more energy than you put in.
The problem is you don't have a single bell. You have $6.023 \times 10^{23}$ bells for every 18g of water and those bells have no mechanism to keep themselves in phase with each other. So when you turn on the microwaves you end up with an equilibrium between absorption and stimulated (and spontaneous) emission. Typically you get roughly equal numbers of dipoles in the ground and excited state.
But actually this still isn't really heating in the sense we normally use the word. Heating occurs when the excited dipoles can relax by transferring their energy to lattice vibrations rather than by emitting a photon. So the overall process is photon $\rightarrow$ excited dipole $\rightarrow$ lattice vibrations = heat. This is more like what happens in a microwave oven. The reverse, i.e. cooling, process is when lattice vibrations cause transient dipoles and these radiate photons. This is just black body radiation.
Best Answer
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.