I have been wanting to tinker with the Raspberry PI to learn more about electromagnetic frequencies; however, before initiating anything, I read the legal debates regarding PiFm. It appears that both Industry Canada and FCC's regulations regarding broadcasting allow for unlicensed operation as long that the field strength and broadcast distance comply with the legal parameters established. That said, I was wondering if anyone has profiled the field strength of PiFm operating on the Raspberry PI 1 Model B without an antenna. Preferably, I would like to know the dBµV/m at exactly 3 meter distance from the PI while running PiFm. If the value is greater than the legal amount set, I will responsibly set the project idea aside.
Also, consider becoming a radio amateur (ham). The entry level exam is no longer that difficult as it once used to be. (I passed it as a kid.) With an amateur radio license you are allowed to run legal RF experiments with much higher power levels. You can ask any ham radio related questions over at https://ham.stackexchange.com/
As you know PiFm is a great bench experiment but a very dirty RF transmitter. While it will produce a noisy output across several frequencies, it will do so with very limited power. The project author reports a range of approximately 10cm without an antenna attached (and 100m with). This will vary depending on your power source, other attachments, noise sources and so on.
A cheap RTL-SDR USB dongle and Gqrx (or similar) software gives a fantastic RF waterfall across a decent range of frequencies. Anyone into radio may scoff, but it gives at least some idea of transmitter behaviour. Taking your own measurements, even bad ones at first, is better than guessing! I use this for debugging my 433MHz devices on a shoestring budget.
Check the local radio band plans for frequency users before experimenting. Exercise caution if you live near an airfield, observatory, etc. In my experience you'll only receive regulatory attention if you annoy someone. Be far more worried about stepping on important frequencies which lives depend on. Or your neighbours' TV :)
The RTL-SDR is useful here too. Monitor frequencies over a period of time before experimenting. Find a wide band of unused frequencies with minimal interference to safely operate in. And check the band plan again to make sure it isn't quiet for a reason ;)
If you get "the bug" I can recommend the RasWIK (Wireless Inventors Kit) for data transmissions, HackRF and Gnuradio for voice/data/repeater/everything else, or cheap 433/315MHz boards and kits available online.
yes software defined radio is a great way to investigate this question, I personally recommend the cheaper RTL-SDR from RTL-SDR blog. It is only $35 and I have been able to see the (nasty) harmonics created by PiFM and an antenna. It gives output dB which you can use.