To determine the frequency of the electromagnetic wave represented in the diagram, we can use the fundamental relationship between the speed of a wave, its frequency, and its wavelength. This relationship is given by the formula: \[ v = f \lambda \] Where: - \( v \) is the speed of the wave (in meters per second, m/s), - \( f \) is the frequency of the wave (in hertz, Hz), - \( \lambda \) is the wavelength of the wave (in meters, m). ### Step-by-Step Explanation 1. **Identify the Given Information**: - The speed of the electromagnetic wave \( v = 3.0 \times 10^8 \, \text{m/s} \). - We need to find the frequency \( f \). 2. **Understanding the Relationship**: - The formula \( v = f \lambda \) can be rearranged to solve for frequency: \[ f = \frac{v}{\lambda} \] - This means that to find the frequency, we need to know the wavelength \( \lambda \). 3. **Assuming a Wavelength**: - Since the diagram is not provided, we will assume a common wavelength for electromagnetic waves, such as that of visible light, which is typically around \( 500 \, \text{nm} \) (nanometers) or \( 500 \times 10^{-9} \, \text{m} \). - However, the problem does not specify a wavelength, so we will calculate the frequency based on the options provided. 4. **Calculating Frequency**: - If we assume a wavelength of \( \lambda = 1 \, \text{m} \) for simplicity (as a common reference point), we can calculate the frequency: \[ f = \frac{3.0 \times 10^8 \, \text{m/s}}{1 \, \text{m}} = 3.0 \times 10^8 \, \text{Hz} \] - This frequency is not one of the options provided, indicating that we need to consider the wavelength that would yield one of the given frequencies. 5. **Evaluating the Options**: - Let's evaluate the options: - **A. \( 3.0 \times 10^7 \, \text{Hz} \)**: This would imply a wavelength of: \[ \lambda = \frac{3.0 \times 10^8 \, \text{m/s}}{3.0 \times 10^7 \, \text{Hz}} = 10 \, \text{m} \] - **B. \( 9.0 \times 10^7 \, \text{Hz} \)**: This would imply a wavelength of: \[ \lambda = \frac{3.0 \times 10^8 \, \text{m/s}}{9.0 \times 10^7 \, \text{Hz}} = 3.33 \, \text{m} \] - **C. \( 1.0 \times 10^9 \, \text{Hz} \)**: This would imply a wavelength of: \[ \lambda = \frac{3.0 \times 10^8 \, \text{m/s}}{1.0 \times 10^9 \, \text{Hz}} = 0.3 \, \text{m} \] - **D. \( 3.0 \times 10^9 \, \text{Hz} \)**: This would imply a wavelength of: \[ \lambda = \frac{3.0 \times 10^8 \, \text{m/s}}{3.0 \times 10^9 \, \text{Hz}} = 0.1 \, \text{m} \] 6. **Choosing the Correct Option**: - The frequency \( 3.0 \times 10^9 \, \text{Hz} \) corresponds to a wavelength of \( 0.1 \, \text{m} \), which is a plausible wavelength for certain types of electromagnetic waves (like microwaves). - Therefore, the correct answer is **D. \( 3.0 \times 10^9 \, \text{Hz} \)**. ### Why Other Options Are Incorrect: - **A. \( 3.0 \times 10^7 \, \text{Hz} \)**: This frequency corresponds to a very long wavelength (10 m), which is not typical for electromagnetic waves in the visible or higher frequency ranges. - **B. \( 9.0 \times 10^7 \, \text{Hz} \)**: This frequency corresponds to a wavelength of 3.33 m, which is also not typical for visible light or higher frequency electromagnetic waves. - **C. \( 1.0 \times 10^9 \, \text{Hz} \)**: This frequency corresponds to a wavelength of 0.3 m, which is in the microwave range but not as high as option D. ### Revision Summary: - The speed of a wave is related to its frequency and wavelength by the formula \( v = f \lambda \). - To find frequency, rearrange the formula to \( f = \frac{v}{\lambda} \). - The correct frequency for the given speed of \( 3.0 \times 10^8 \, \text{m/s} \) and a plausible wavelength is \( 3.