What is the fundamental frequency of the radio waves of a standing wave pattern?

Question by Naysayer: What is the fundamental frequency of the radio waves of a standing wave pattern?
A standing-wave interference pattern is set up by radio waves between two metal sheets d= 1.76 m apart. This is the shortest distance between the plates that will produce a standing-wave pattern. What is the fundamental frequency of the radio waves?

Best answer:

Answer by kiwiJOEY
Remember that the speed of any wave is equal to the frequency times the wavelength, v = f?.

And in any standing wave which has a node at both ends (which must occur since the wave will be ‘fixed’ at both ends, i.e. not free to move at the ends) including a radio wave, the fundamental occurs when the length of the standing wave interference pattern is exactly half a wavelength long, and since the length of this standing wave interference pattern is 1.76 m, this tells you the wavelength of the wave is 2 x 1.76 m = 3.52 m.

Also the speed of the wave will be the speed of any radio wave, which is the same as the speed of light, 3 x 10^8 m/s.

f = v/?, frequency is speed divided by wavelength. So the frequency of the fundamental is
f = (3 x 10^8 m/s)/(3.52) = 8.52 x 10^7 s^-1 = 8.52 x 10^7 Hz = 85.2 MHz.

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