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don't know where you got that part... What about the telescope antennas that you find on radios and old TV sets? they can be put at any length the user wishes, doesn't change the frequency it receives...
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The length of the antennae is for transmission, not recieving. It must be at least 1/4 the wavelength to transmit, 1/2 for decent quality. The 1/2 is because the transmitter grounds itself (through the casing) so you only require half the sine wave.
This is important because cell phones dont just recieve, but transmit. These do increase receiving, but as far as transmitting goes it wouldnt increase anything.
To recieve it requires area and height. When you see recieving stations there are usually one big antennae with 3-4 small ones around, all connected. The big one is for transmitting and the small ones that are connected provide an "area" for recieving. You dont need a sheet, but just a triangle/circle of wire, and it acts just like a metal sheet would as far as quality goes. So yes, the little thing would increase surface area to aid in recieving, but no it wouldnt change transmitting.
... god I hate calc-based physics... go through all those sleepless nights and this is the first time I've ever used ANY of it.