I'm not sure if it counts as an official study or not (probably not) but there was a program on TV a while back here where they got a few volunteers and put a portable mobile phone mast outside where they were staying for the week. They were told it would be off for the first half of the week and on for the second, however the reverse was actually true, it was on for the first and off for the second. In the first half of the week everyone felt fine, in the second half a few people began to complain they weren't feeling well...
That to me says it all!
well typically the higher up you go in frequency the more energy the waves can carry once it reaches a certain energy level the rf waves become ionising radiation and thats the type that can cause more harm but that dosent happen till you get to X ray frequencies its some complicated psyhics that i dont fully understand so im going to stop here
In conventional physics yes, the shorter the wavelength (higher the frequency) the more penetrating the waves get and therefore their ability to do harm goes up. This doesn't always hold true practically however and once you start getting into wave-particle duality things really get rather complicated and interesting (especially since it's something that no-one fully understands, which is part of the reason why we have these scares in the first place!)