(a) To find the wave frequency, we can use the relationship between the speed of light (c), wavelength (λ), and frequency (f). The speed of light in a vacuum is approximately $3 \times 10^8 \, \text{m/s}$.

$$ c = \lambda \cdot f $$

Rearranging to solve for frequency (f):

$$ f = \frac{c}{\lambda} $$

Given:
$$ \lambda = 484 \, \text{m} $$
$$ c = 3 \times 10^8 \, \text{m/s} $$

$$ f = \frac{3 \times 10^8 \, \text{m/s}}{484 \, \text{m}} $$

$$ f \approx 6.20 \times 10^5 \, \text{Hz} $$

So, the frequency of the wave is approximately $620 \, \text{kHz}$.

(b) To find the amplitude of the wave's magnetic field, we use the relationship between the electric field (E) and the magnetic field (B) in an electromagnetic wave:

$$ E = c \cdot B $$

Rearranging to solve for B:

$$ B = \frac{E}{c} $$

Given:
$$ E = 347 \, \text{mV/m} = 347 \times 10^{-3} \, \text{V/m} $$
$$ c = 3 \times 10^8 \, \text{m/s} $$

$$ B = \frac{347 \times 10^{-3} \, \text{V/m}}{3 \times 10^8 \, \text{m/s}} $$

$$ B \approx 1.16 \times 10^{-9} \, \text{T} $$

So, the amplitude of the wave's magnetic field is approximately $1.16 \, \text{nT}$.

(c) The direction of the magnetic field in an electromagnetic wave can be determined using the right-hand rule. For a wave propagating due east (positive x-direction) with a vertically polarized electric field (positive y-direction), the magnetic field will be in the direction that completes the right-handed coordinate system.

Using the right-hand rule:
- Point your thumb in the direction of wave propagation (east, or positive x-direction).
- Point your index finger in the direction of the electric field (vertical, or positive y-direction).

Your middle finger, perpendicular to both, will point in the direction of the magnetic field. In this case, it will point south (negative z-direction).

So, the direction of the magnetic field is south.

Question

(a) To find the wave frequency, we can use the relationship between the speed of light (c), wavelength (λ), and frequency (f). The speed of light in a vacuum is approximately $3 \times 10^8 \, \text{m/s}$.

$$ c = \lambda \cdot f $$

Rearranging to solve for frequency (f):

$$ f = \frac{c}{\lambda} $$

Given:
$$ \lambda = 484 \, \text{m} $$
$$ c = 3 \times 10^8 \, \text{m/s} $$

$$ f = \frac{3 \times 10^8 \, \text{m/s}}{484 \, \text{m}} $$

$$ f \approx 6.20 \times 10^5 \, \text{Hz} $$

So, the frequency of the wave is approximately $620 \, \text{kHz}$.

(b) To find the amplitude of the wave's magnetic field, we use the relationship between the electric field (E) and the magnetic field (B) in an electromagnetic wave:

$$ E = c \cdot B $$

Rearranging to solve for B:

$$ B = \frac{E}{c} $$

Given:
$$ E = 347 \, \text{mV/m} = 347 \times 10^{-3} \, \text{V/m} $$
$$ c = 3 \times 10^8 \, \text{m/s} $$

$$ B = \frac{347 \times 10^{-3} \, \text{V/m}}{3 \times 10^8 \, \text{m/s}} $$

$$ B \approx 1.16 \times 10^{-9} \, \text{T} $$

So, the amplitude of the wave's magnetic field is approximately $1.16 \, \text{nT}$.

(c) The direction of the magnetic field in an electromagnetic wave can be determined using the right-hand rule. For a wave propagating due east (positive x-direction) with a vertically polarized electric field (positive y-direction), the magnetic field will be in the direction that completes the right-handed coordinate system.

Using the right-hand rule:
- Point your thumb in the direction of wave propagation (east, or positive x-direction).
- Point your index finger in the direction of the electric field (vertical, or positive y-direction).

Your middle finger, perpendicular to both, will point in the direction of the magnetic field. In this case, it will point south (negative z-direction).

So, the direction of the magnetic field is south.

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