Question
(a) The ideal size (most efficient) for a broadcast antenna with one end on the ground is one-fourth the wavelength ($\dfrac{\lambda}{4}$) of the electromagnetic radiation being sent out. If a new radio station has such an antenna that is 50.0 m high, what frequency does it broadcast most efficiently? Is this in the AM or FM band? (b) Discuss the analogy of the fundamental resonant mode of an air column closed at one end to the resonance of currents on an antenna that is one- fourth their wavelength.
1. $1.50 \times 10^6 \textrm{ Hz}$. This is in the AM band.
2. Resonance for an electromagnetic wave at $\lambda_1 = \dfrac{h}{4}$ is analogous to sound resonance in a closed end tube which also has $\lambda_1 = \dfrac{L}{4}$. $h$ is analogous to $L$. Further resonances for the antenna might occur at $f_n = \dfrac{nc}{4h}, n=1, 3, 5, ...$
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