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Default DirecTV dish-- F/? and dB gain?

I have been wanting to try some silly experiments using a digital TV
dish to make a super-hearing type thing for a while, and finally got
ahold of one from someone's trash.

The one I found has the mounting pole and horn bracket, but the feed
horn is missing. Even so just looking at photos of them online, it
doesn't appear to me that the horn is at the geometric focal point.
Also--even considering it's an offset dish--the dish appears rather
shallow and has a round profile, not a parabola at all. Do RF waves
behave differently than sound waves in this regard? (Would RF waves have
a shorter F-length than simple geometry would indicate?)

Also just for trivia purposes I am curious as to what the typical dB
gain is for this sort of dish (when used for RF), and if that equates at
all to sound waves...
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