Electromagnetic Waves Physics Example 4

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Example 4

hard
A WiFi router transmits at 5 GHz5 \text{ GHz} with a power of 0.1 W0.1 \text{ W}. What is the wavelength? If the signal spreads uniformly in all directions, what is the intensity at 10 m10 \text{ m}? Use c=3×108 m/sc = 3 \times 10^8 \text{ m/s}.

Solution

  1. 1
    Frequency: 5 GHz=5×109 Hz5 \text{ GHz} = 5 \times 10^9 \text{ Hz}. Wavelength: λ=cf=3×1085×109=0.06 m=6 cm\lambda = \frac{c}{f} = \frac{3 \times 10^8}{5 \times 10^9} = 0.06 \text{ m} = 6 \text{ cm}.
  2. 2
    For uniform radiation in all directions, intensity decreases as I=P4πr2I = \frac{P}{4\pi r^2}.
  3. 3
    I=0.14π(10)2=0.11256.67.96×105 W/m2I = \frac{0.1}{4\pi(10)^2} = \frac{0.1}{1256.6} \approx 7.96 \times 10^{-5} \text{ W/m}^2

Answer

λ=6 cm,I8×105 W/m2\lambda = 6 \text{ cm}, \quad I \approx 8 \times 10^{-5} \text{ W/m}^2
WiFi signals are electromagnetic waves in the microwave band. Signal intensity follows the inverse-square law — doubling the distance reduces the intensity to one-quarter.

About Electromagnetic Waves

Transverse waves consisting of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation.

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