Question

The minimum length of an antenna to transmit a signal of frequency \( 3 \text{ kHz} \) is

• A. 20 km
• B. 25 km
• C. 50 km
• D. 75 km

Hint:

Use the relation \( L = \frac{c}{4f} \) for the minimum antenna length, where \( c \) is the speed of light.

Answer 1

The Correct Option is B

The minimum length \( L \) of a transmitting antenna is given by: \[ L = \frac{\lambda}{4} \quad \text{where } \lambda = \frac{c}{f} \] Given: \[ f = 3 \times 10^3 \text{ Hz}, \quad c = 3 \times 10^8 \text{ m/s} \] \[ \lambda = \frac{3 \times 10^8}{3 \times 10^3} = 10^5 \text{ m} \Rightarrow L = \frac{10^5}{4} = 2.5 \times 10^4 = 25 \text{ km} \]