To calculate the frequency and period of the radiation emitted by Project Seafarer, we'll use the following relationships involving wavelength, frequency, and period:

1. Speed of light ($c$): Approximately $3.00 \times 10^8$ m/s.
2. Wavelength ($\lambda$): Given as $1.5 \times 10^2$ Earth radii.

Step 1: Calculate the Wavelength

The Earth's radius is $6370$ km, so:

$\lambda = 1.5 \times 10^2 \times 6370 \text{ km}$ $\lambda = 1.5 \times 100 \times 6370 \text{ km} = 955500 \text{ km} = 955500 \times 10^3 \text{ m} = 9.555 \times 10^8 \text{ m}$

Step 2: Calculate Frequency ($f$)

Using the relationship:

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

Substituting in the values:

$f = \frac{3.00 \times 10^8 \text{ m/s}}{9.555 \times 10^8 \text{ m}} \approx 0.314 \text{ Hz}$

Step 3: Calculate Period ($T$)

The period is the reciprocal of frequency:

$T = \frac{1}{f} = \frac{1}{0.314} \approx 3.18 \text{ s}$

Summary of Results

(a) Frequency: $f \approx 0.314 \text{ Hz}$

(b) Period: $T \approx 3.18 \text{ s}$

If you have any questions or need further details, feel free to ask! Here are some related questions you might consider:

1. What are the implications of this frequency for submarine communication?
2. How does seawater's conductivity affect electromagnetic wave propagation?
3. What other frequencies are typically used in submarine communication?
4. How would the design of antennas change for different wavelengths?
5. What are some practical challenges in constructing such a large antenna?

Tip: Always ensure that the wavelength used in calculations is in the correct unit (meters) for consistency with speed and frequency calculations.