As Eric Alper recently pointed out on Twitter, A$AP Rocky's song "F**kin Problems" is the latest in a string of songs that have the word "f**k" (or some variation thereof) in their title to reach the Top 10 on Billboard's Hot 100 singles chart (the other two recent hits were Pink's "F**kin’ Perfect" & Cee-Lo's "F**k You!"). So far as I can tell, the first such song to achieve that, um, distinction was Eamon's "F**k It (I Don't Want You Back)", which hit number seven back in 2004 (the "answer" song by Frankee, entitled "F.U.R.B. (F**k You Right Back)" only hit number 29 on the Billboard charts - though both songs evidently hit #1 in the UK). Anyone listening to those songs on Canadian radio are unlikely to hear "dirty" versions of them - instead, the broadcast version will likely be an edited version which somehow obscures the profanity, either by substituting a "clean" word, an obscuring sound (the classic "bleep") or altering or dropping the audio on the vocal track when the profanity is said (in almost all such cases, the record company in question will have released an authorized "clean" version of the track for radio play). Are radio stations prohibited by law from broadcasting profanity?
Not really - there isn't, strictly speaking, a legal prohibition on playing unedited versions of songs which containing profanity, but depending on the context it can be a violation of a broadcaster's obligations under the code of ethics which broadcasters agree to observe. (As an aside, I seem to recall that not only was a "clean" version of Nine Inch Nails' "Closer" (which features a fairly prominent use of the f-word in its bridge) the only version you could hear on Canadian radio when it was released in 1994, but it often wasn't even played until after 9pm. Kids these days, with all their hippin' and their hoppin'... .) The Canadian Broadcast Standards Council (CBSC), a non-governmental organization, administers the various codes promulgated by the Canadian Association of Broadcasters (CAB). As a condition of their broadcasting license from the Canadian Radio-television and Telecommunications Commission (CRTC), broadcasters are generally obliged to abide by the CAB codes, one of which is the CAB Code of Ethics, Section 9 of which provides that "particular care shall be taken by radio broadcasters to ensure that programming on their stations does not contain ... unduly coarse and offensive language".
It turns out that Canadian radio stations and television stations broadcast the f-word more than you'd think, at least if the number of complaints the CBSC receives is any indication - a search of the CBSC's online repository of decisions turns up more than sixty decisions stemming from listerner complaints. The 2005 decision regarding the Tragically Hip song "Locked in the Trunk of a Car" (CBSC Decision 04/05-0324) contains a handy review of CBSC decisions regarding the use of the f-word in songs (evidently the first such decision was made in 2001) - some highlights:
the CBSC has "consistently ruled that broadcast of the f-word on radio during daytime and early evening hours [when children are most likely to be listening] constitutes a breach of the CAB Code of Ethics"
repeated use of the f-word in a song can be a violation, but so can a single "gratuitous" use of the f-word (see CBSC Decision 00/01-0670)
The obvious implication of the wording of the statement in the first bullet above is that there may be hours of the day when broadcasting the f-word is not violative of Section 9 of the Code of Ethics. The CBSC panel also noted that "language usage is constantly in a state of evolution... Formerly unacceptable language gradually but invariably insinuates itself into more common usage and a review of the old and new practice is merited from time to time", and so revisiting the treatment of the f-word and its derivatives (which the panel notes appears "in noun, verb, adjective, adverb and interjection forms in English") is occasionally warranted. That being said, in 2008 the CBSC reiterated that broadcasting the f-word in a song played at around 5:15pm violated the Code (CBSC Decision 06/07-1118). In 2011, the CBSC held that the playing of a song (Buckcherry's "Crazy B***h") which edited out the f-word (by dropping the audio) was not a violation of the Code (CBSC Decision 10/11-1169).
So where do we stand? Playing a song featuring unedited uses of the "f-word" during the day and early evening hours is almost certainly still a violation of the CAB Code of Ethics prohibition on the use of coarse language. Broadcasts of the same song at night may not be violations of the Code, but the CBSC does not yet appear to have pronounced definitively on the matter - but broadcasts at such times are less likely, by virtue of the demographics of the listeners, to attract complaints and so we may never actually get a definitive pronouncement.