It turns out that cats have two different purrs-- the contented one and a more urgent one that has a stronger level of a certain high-frequency sound. This study found that cats use the "soliciting purr" when they want to be fed.
Recordings and a video of the purring here.
I'm not surprised; my cat does have a different purr when she wants something.
Incidentally this reminds me of when I was a Gong Frosh in college, charged with protecting the mallet that the Lloyd House President used to beat the our gong every night at dinner. Somebody stole the mallet and left a list of demands to be fulfilled for its return, and one requirement was that Sandip (the other Gong Frosh) and I had to follow the House President around for a while. Whenever he greeted anybody, Sandip had to bark and I had to purr. It wasn't easy.
Later I discovered that my own roommate had been in on the mallet-stealing plot. It's been thirteen years, but I haven't forgotten. Oh, no. I have not forgotten.