What should be the size of the antenna or aerial ? How the power radiated is related to length of the antenna and wavelength ?

Solution :Size of antenna (or) aerial : For TRANSMITTING a signal , we need an antenna . The size of the antenna comparable to the wavelength of the signal (at least `lambda//4`) . So that the antenna properly senses the time VARIATION of the signal . For an e.m waves of FREQUENCY 20 kHz, the wavelength `lambda` is 15 km . Obviously such a long antenna is not possible to construct and operate . There is a need of translating the information contained in our original low frequency base band signal into high frequencies before transmission .
Effective POWER RADIATED by an antenna : A linear (length l) show that the power radiated is proportional to `(l)/(lambda^(2))` . For the same antenna length , the power radiated increases with decreasing `lambda` i.e, increasing frequency .Hence the effective power radiated by a long wavelength base band signal would be small .