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Electromagnetic waves, such as the ones emitted by a cellular phone, are characterized by their frequency. The frequency of a wave is the number of complete wave cycles that pass a given point per second. It's denoted by the symbol \( f \) and is measured in Hertz (Hz).
Calculating the frequency involves knowing the wavelength, which is the distance between successive crests of a wave. In our exercise, the wavelength \( \lambda \) is given as 35.4 cm. To work with it in equations, it must be converted to meters: \( \lambda = 0.354 \text{ m} \).
Since the speed of light \( c \) is a constant \( 3 \times 10^8 \text{ m/s} \) for all electromagnetic waves in a vacuum, the frequency can be determined using the formula:

• \( f = \frac{c}{\lambda} \)

By plugging in the values, we find the frequency to be approximately \( 8.47 \times 10^8 \text{ Hz} \). This value tells us how rapidly the wave oscillates in space, an important characteristic of electromagnetic waves.

The magnetic field amplitude \( B \) describes the strength of the magnetic field in the electromagnetic wave. Electromagnetic waves have both electric and magnetic fields. These fields oscillate perpendicular to each other and to the direction of wave propagation.
Electric field amplitude \( E \) can help calculate the magnetic field amplitude using the wave speed. The speed of light \( c \) sets the relationship between these amplitudes, given by the equation:

• \( c = \frac{E}{B} \)

Rearranging this formula allows us to solve for \( B \):

• \( B = \frac{E}{c} \)

By substituting the given value for the electric field amplitude \( E = 5.40 \times 10^{-2} \text{ V/m} \) and the speed of light, we find that \( B \approx 1.80 \times 10^{-10} \text{ T} \). This shows how weak the magnetic field component is compared to the electric field in such electromagnetic waves.

The intensity of an electromagnetic wave indicates how much energy the wave conveys per unit time per unit area. It is a crucial factor in understanding the power of a wave.
The expression for intensity \( I \) of an electromagnetic wave is:

• \( I = \frac{1}{2} \epsilon_0 c E^2 \)

Here \( \epsilon_0 \), the vacuum permittivity, is a constant \( 8.85 \times 10^{-12} \text{ F/m} \). By inserting the known values for \( E \), \( c \), and \( \epsilon_0 \) into the equation, we can compute the intensity:
\[ I = \frac{1}{2} (8.85 \times 10^{-12}) (3 \times 10^8) (5.40 \times 10^{-2})^2 \]
Leading to an intensity of approximately \( 3.88 \times 10^{-3} \text{ W/m}^2 \).
This value gives us a measure of how much electromagnetic energy is passing through a square meter of area in one second.