Is it possible to receive transmissions from a radio station operating at a wavelength of 100 m with a receiving oscillating circuit consisting of a coil with an inductance of 0.001 H and a capacitor with a capacity of 10 pF?
Frequency of oscillations in the circuit:
ν = 1 / (2П√ (LC));
L is the inductance of the coil, C is the capacitance of the capacitor.
The wavelength λ and the frequency of electromagnetic waves ν are related by the relationship:
λ = c / ν, where c is the speed of light.
λ = c / (1 / (2П√ (LC))) = с * 2П√ (LC)) =
= 3 * 10 ^ 8 m / s * 2 * 3.14 * √ (0.001 H * 10 * 10 ^ (- 12) F) = 188 m.
Answer. It is impossible to receive radio transmissions using the specified receiver, because it is tuned to a wavelength of λ = 188 m, and not 100 m.
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