From what wavelength can radiation go through a human body without very much changing? Gamma-rays can go through a body but they will ionize a lot of atoms (I don't know whether some of the gamma photons will go through without any interaction at all?). The same for X-rays. Visible light and infrared (till $1mm$) probably only reflects and absorbs. But perhaps rays from 1 cm and longer (radiowaves) can get through the human body without harming the body or without changing in frequency?
 A: There are two effects of electromagnetic  waves on human body.


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*Heating effects, occurring mostly around 2.45 GHz (which is the frequency used in microwave ovens)

*Ionizing effects, which can damage human body and cells


Here is a picture of how the radiowaves penetrate the human body according to the frequency.
The legend is from 1 to 10 : Cosmic rays, gamma rays, X-rays, ultraviolet, visible spectrum, infrared, microwaves, radiowaves, very low frequencies, extremely low frequencies. 

A: There's no uniform relationship between wavelength and extent of penetration/absorption. It's a quite complex function of both wavelength and material.
There are examples of low as well as high frequencies which penetrate, as well as some middle ones that don't. Also, from among the penetrating ones, some are also absorbed, some not.
Regarding health, general scientific consensus is that penetrating ones harm only if they are ionizing or heat the body to the extreme.
The image in MaximGi's answer seems fine, here are 2 more references I could find:
https://www.researchgate.net/figure/a-Tissue-penetration-depth-of-light-with-different-wavelengths-NIR-light-penetrates_fig13_316712743
https://www.semanticscholar.org/paper/Evaluation-of-absorbed-light-dose-in-human-skin-by-Chang-Huang/fc946510ccb0b616fa66ab7d7324197564492533
