Question

Size of the antenna for a carrier wave of frequency 3 MHz is:

• A. 75 m
• B. 50 m
• C. 2.5 m
• D. 25 m

Hint:

Use the formula \( \lambda = \frac{c}{f} \) to calculate the wavelength and determine the size of the antenna.

Answer 1

The Correct Option is D

To determine the size of the antenna for a carrier wave of a given frequency, we use the relationship between the wavelength of the wave and the size of the antenna. The optimal length of an antenna is typically a fraction (often \(\frac{1}{4}\) or \(\frac{1}{2}\)) of the wavelength of the carrier wave. Given:
- Frequency of the carrier wave, \( f = 3 \, \text{MHz} = 3 \times 10^6 \, \text{Hz} \) Step 1: Calculate the Wavelength The wavelength \( \lambda \) of the wave is given by: \[ \lambda = \frac{c}{f} \] where \( c \) is the speed of light (\( c \approx 3 \times 10^8 \, \text{m/s} \)). \[ \lambda = \frac{3 \times 10^8}{3 \times 10^6} = 100 \, \text{m} \] Step 2: Determine the Antenna Size For an efficient antenna, the length is typically \(\frac{1}{4}\) of the wavelength: \[ \text{Antenna length} = \frac{\lambda}{4} = \frac{100}{4} = 25 \, \text{m} \] Final Answer: \[ \boxed{25 \, \text{m}} \] This corresponds to option (4).