Question

A radio can tune to any station in $6\, MHz$ to $10\, MHz$ band The value of corresponding wavelength bandwidth will be :

• A. 4 m
• B. 20 m
• C. 30 m
• D. 50 m

Answer 1

The Correct Option is B

 To determine the wavelength bandwidth corresponding to a frequency bandwidth of 6 MHz to 10 MHz, we need to understand the relationship between frequency and wavelength. This relationship is given by the formula:

\(c = \lambda \cdot f\)

where:

• \(c\) is the speed of light, approximately \(3 \times 10^8 \, \text{m/s}\)
• \(\lambda\) is the wavelength in meters
• \(f\) is the frequency in hertz (Hz)

First, convert the given frequencies from MHz (megahertz) to Hz (hertz):

• 6 MHz = \(6 \times 10^6 \, \text{Hz}\)
• 10 MHz = \(10 \times 10^6 \, \text{Hz}\)

Using the formula, calculate the corresponding wavelengths:

• For \(f_1 = 6 \times 10^6 \, \text{Hz}\):
  • \(\lambda_1 = \frac{c}{f_1} = \frac{3 \times 10^8}{6 \times 10^6} = 50 \, \text{m}\)
• For \(f_2 = 10 \times 10^6 \, \text{Hz}\):
  • \(\lambda_2 = \frac{c}{f_2} = \frac{3 \times 10^8}{10 \times 10^6} = 30 \, \text{m}\)

The wavelength bandwidth is the difference between the two wavelengths:

• \(\Delta \lambda = \lambda_1 - \lambda_2 = 50 \, \text{m} - 30 \, \text{m} = 20 \, \text{m}\)

Therefore, the correct answer is 20 m, which corresponds to the wavelength bandwidth between the given frequency range.