Question

A radio can tune in to any station in the 7.5 MHz to 12 MHz band. The corresponding wavelength band is

• A. 75m-12m
• B. 22.5m-36m
• C. 40m-25m
• D. 20m-45m

Hint:

Wavelength and frequency are inversely proportional. The highest frequency corresponds to the shortest wavelength and vice-versa.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Electromagnetic waves, such as radio waves, travel at the speed of light in vacuum.
The relationship between frequency, wavelength, and the speed of light is given by the wave equation.

Step 2: Key Formula or Approach:
Speed of light \(c = \nu \lambda\), where \(\nu\) is frequency and \(\lambda\) is wavelength.
Given \(c = 3 \times 10^8\) m/s.

Step 3: Detailed Explanation:
1. For lower frequency \(\nu_1 = 7.5 \text{ MHz} = 7.5 \times 10^6 \text{ Hz}\):
\[ \lambda_1 = \frac{c}{\nu_1} = \frac{3 \times 10^8}{7.5 \times 10^6} \]
\[ \lambda_1 = \frac{300 \times 10^6}{7.5 \times 10^6} = \frac{300}{7.5} = 40 \text{ m} \]
2. For higher frequency \(\nu_2 = 12 \text{ MHz} = 12 \times 10^6 \text{ Hz}\):
\[ \lambda_2 = \frac{c}{\nu_2} = \frac{3 \times 10^8}{12 \times 10^6} \]
\[ \lambda_2 = \frac{300 \times 10^6}{12 \times 10^6} = \frac{300}{12} = 25 \text{ m} \]
The wavelength range corresponding to 7.5 MHz - 12 MHz is 40 m - 25 m.

Step 4: Final Answer:
The corresponding wavelength band is 40m-25m.