Problem — Fermi estimate for an FM station

Problem

You are at $d=20$ km from an FM station broadcasting at $f=100$ MHz. Estimate how many wavelengths separate the transmitter and receiver, and how long the radiation takes to cover them.

Solution

Wavelength.

$\lambda=\frac{c}{f}=\frac{3{,}00\cdot 10^8}{100\cdot 10^6}=3\ \text{m}$

Number of wavelengths.

$N=\frac{d}{\lambda}=\frac{20000}{3}\approx 6{,}7\cdot 10^3$

Travel time.

$t=\frac{d}{c}=\frac{20000}{3{,}00\cdot 10^8}\approx 6{,}7\cdot 10^{-5}\ \text{s}$

$\ev{N\approx 6{,}7\cdot 10^3,\qquad t\approx 67\ \mu\text{s}}$

Collegamenti

Argomenti: Onde elettromagnetiche Concetti: Onda elettromagnetica Competenze: Stime di Fermi