Question

What should be the length of antenna for a carrier wave of frequency \(6 \times 10^{8}\,\text{Hz}\)? (Given: velocity of light \(c = 3 \times 10^{8}\,\text{m/s}\))

• A. \(0.250\,\text{m}\)
• B. \(0.062\,\text{m}\)
• C. \(0.125\,\text{m}\)
• D. \(0.031\,\text{m}\)

Hint:

Antenna length is usually taken as \(\lambda/4\) for maximum radiation.

Answer 1

The Correct Option is C

Step 1: Calculating wavelength of the carrier wave.
\[ \lambda = \frac{c}{f} = \frac{3 \times 10^8}{6 \times 10^8} = 0.5\,\text{m} \]
Step 2: Length of antenna.
For efficient transmission, antenna length is
\[ L = \frac{\lambda}{4} \]
Step 3: Substituting value of \(\lambda\).
\[ L = \frac{0.5}{4} = 0.125\,\text{m} \]
Step 4: Conclusion.
The required antenna length is \(0.125\,\text{m}\).