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To calculate the frequency of an electromagnetic wave, we use the fundamental relationship between frequency, wavelength, and the speed of light. This relationship is commonly expressed by the equation \( c = \lambda f \), where \( c \) is the speed of light, \( \lambda \) is the wavelength, and \( f \) is the frequency.
First, ensure that the wavelength is in meters. In our problem, the given wavelength is 35.4 cm, which is 0.354 meters.
Now, plug the values into the rearranged formula to find frequency: \( f = \frac{c}{\lambda} \).
Using the speed of light, \( c = 3 \times 10^8 \text{ m/s} \), and the converted wavelength, \( \lambda = 0.354 \text{ m}\), the frequency \( f \) is computed as follows:

• \( f = \frac{3 \times 10^8}{0.354} \approx 8.474 \times 10^8 \text{ Hz} \)

This frequency tells us the number of wave cycles that pass a given point per second. Understanding this concept is crucial for analyzing electromagnetic waves and their interactions.

Wave intensity describes how much energy is transmitted by the wave over a specific area and time. For electromagnetic waves, intensity (\( I \)) can be derived from the electric-field amplitude (\( E_0 \)).
The formula to compute intensity is:

• \( I = \frac{E_0^2}{2\mu_0 c} \)

Where \( \mu_0 \) is the permeability of free space \( (4\pi \times 10^{-7} \text{ Tm/A}) \) and \( c \) is the speed of light.
Substituting the values of the electric-field amplitude \( (5.40 \times 10^{-2} \text{ V/m}) \), we calculate:

• \( I = \frac{(5.40 \times 10^{-2})^2}{2 \times 4\pi \times 10^{-7} \times 3 \times 10^8} \approx 3.87 \times 10^{-3} \text{ W/m}^2 \)

This intensity measure is pivotal for applications where energy transfer is crucial, such as in wireless communications and power beaming.

In an electromagnetic wave, electric fields and magnetic fields are interlinked. The magnetic-field amplitude \( (B_0) \) can be derived from the given electric-field amplitude \( (E_0) \) using the relationship:

• \( B_0 = \frac{E_0}{c} \)

The speed of light \( c \) is a constant \( (3 \times 10^8 \text{ m/s}) \). For the electric-field amplitude provided as \( (5.40 \times 10^{-2} \text{ V/m}) \), you can calculate the magnetic-field amplitude as follows:

• \( B_0 = \frac{5.40 \times 10^{-2}}{3 \times 10^8} = 1.8 \times 10^{-10} \text{ T} \)

This magnetic-field amplitude is key in understanding the magnetic component of electromagnetic waves and helps in applications like magnetic resonance imaging (MRI) and radio broadcasting.