And those tones are: Middle C (the short opening and closing tones) and a long note middle-way between G#5 and A5 (played before the announcement--probably some thousands of Hertz).
I wonder, are these tones nationally standardized across weather stations, or do your radio weather alerts sound different than mine? Same computerized voice?
I wasn't sure what picture to post this time, so I went with what I thought was cool: shots of doppler radar stations. Enjoy.