How does EM radiation damage change with frequency?

The answer is that as the wavelength of radiation, light - EM radiation, gets shorter, in other words the frequency increases, then it packs a more energetic punch. At long wavelengths like radio waves and microwaves, we regard this radiation as non-ionising. In other words, when it impacts on something, it does not have enough energy to physically disrupt the bonds that connect atoms together. For that reason, it means that when you are hit by this radiation, it will warm up your tissue because it will make the particles vibrate more and get hotter, but it will not physically break the bonds between them, so it should not trigger, for instance, mutations in DNA that could cause cancer. As you go into shorter and shorter wavelengths of radiation, so you go beyond UV and you're into x-rays and then gamma rays, this is light with a very high frequency, very short wavelength where the light has sufficient energy to physically disrupt chemical bonds. It literally breaks the bonds between atoms. This means you can introduce changes to your DNA, you can introduce damage to material in cells which can put stress on cells, damage tissue, and it can also introduce cancer causing mutations. That's why we worry about ionising short wavelength radiation. We're less concerned about holding a mobile phone to our head because that's microwaves which are not said to be ionising.