TV channel 2 broadcasts in the frequency range 52 to 61 MHz. What is the corresponding range of wavelengths? (Let us denote the minimum and maximum wavelengths by Amin and Amax, respectively.) Amin Amax
TV channel 2 broadcasts in the frequency range 52 to 61 MHz. What is the corresponding range of wavelengths? (Let us denote the minimum and maximum wavelengths by Amin and Amax, respectively.) Amin Amax
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Problem Statement:**
TV channel 2 broadcasts in the frequency range of 52 to 61 MHz. What is the corresponding range of wavelengths? (Let us denote the minimum and maximum wavelengths by λ_min and λ_max, respectively.)
**Input Fields:**
λ_min = [______]
λ_max = [______]
In this problem, we need to find the minimum and maximum wavelengths corresponding to the given frequency range. The relationship between the frequency (f) and the wavelength (λ) of an electromagnetic wave is given by the equation:
\[ \lambda = \frac{c}{f} \]
where:
- \( \lambda \) is the wavelength,
- \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) meters per second),
- \( f \) is the frequency.
**Steps to Solve:**
1. Convert the given frequency range from MHz to Hz:
- \( 52 \text{ MHz} = 52 \times 10^6 \text{ Hz} \)
- \( 61 \text{ MHz} = 61 \times 10^6 \text{ Hz} \)
2. Use the formula \( \lambda = \frac{c}{f} \) to find the wavelengths corresponding to the minimum and maximum frequencies:
- For \( f_{\text{min}} = 52 \times 10^6 \text{ Hz} \):
\[
\lambda_{\text{max}} = \frac{3 \times 10^8 \text{ m/s}}{52 \times 10^6 \text{ Hz}}
\]
- For \( f_{\text{max}} = 61 \times 10^6 \text{ Hz} \):
\[
\lambda_{\text{min}} = \frac{3 \times 10^8 \text{ m/s}}{61 \times 10^6 \text{ Hz}}
\]
**Explanation of Fields:**
- **λ_min**: This is the minimum wavelength corresponding to the highest frequency in the given range.
- **λ_max**: This is the maximum wavelength corresponding to the lowest frequency in the given range.
**Note:** Ensure to maintain proper units and significant figures while performing the calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2379bb0-49c5-44f7-ac7a-000baa150133%2F323bc883-76b4-48bb-a1b8-6e411f53c88c%2Fa7pp00g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
TV channel 2 broadcasts in the frequency range of 52 to 61 MHz. What is the corresponding range of wavelengths? (Let us denote the minimum and maximum wavelengths by λ_min and λ_max, respectively.)
**Input Fields:**
λ_min = [______]
λ_max = [______]
In this problem, we need to find the minimum and maximum wavelengths corresponding to the given frequency range. The relationship between the frequency (f) and the wavelength (λ) of an electromagnetic wave is given by the equation:
\[ \lambda = \frac{c}{f} \]
where:
- \( \lambda \) is the wavelength,
- \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) meters per second),
- \( f \) is the frequency.
**Steps to Solve:**
1. Convert the given frequency range from MHz to Hz:
- \( 52 \text{ MHz} = 52 \times 10^6 \text{ Hz} \)
- \( 61 \text{ MHz} = 61 \times 10^6 \text{ Hz} \)
2. Use the formula \( \lambda = \frac{c}{f} \) to find the wavelengths corresponding to the minimum and maximum frequencies:
- For \( f_{\text{min}} = 52 \times 10^6 \text{ Hz} \):
\[
\lambda_{\text{max}} = \frac{3 \times 10^8 \text{ m/s}}{52 \times 10^6 \text{ Hz}}
\]
- For \( f_{\text{max}} = 61 \times 10^6 \text{ Hz} \):
\[
\lambda_{\text{min}} = \frac{3 \times 10^8 \text{ m/s}}{61 \times 10^6 \text{ Hz}}
\]
**Explanation of Fields:**
- **λ_min**: This is the minimum wavelength corresponding to the highest frequency in the given range.
- **λ_max**: This is the maximum wavelength corresponding to the lowest frequency in the given range.
**Note:** Ensure to maintain proper units and significant figures while performing the calculations.
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