Question

The length of antenna required to transmit the signals of frequency \( 1.5 \times 10^8 \) Hz is [velocity of light in air, \( c = 3 \times 10^8 \, \text{m/s} \)]

• A. 50 cm
• B. 40 cm
• C. 50 m
• D. 20 cm

Hint:

The length of an antenna is inversely proportional to the frequency of the signal. For transmitting signals, it is typically half the wavelength.

Answer 1

The Correct Option is A

Step 1: Formula for Antenna Length.
The length \( L \) of an antenna required to transmit a signal of frequency \( f \) is given by the formula: \[ L = \frac{c}{2f} \] where \( c \) is the velocity of light and \( f \) is the frequency. Substituting the values: \[ L = \frac{3 \times 10^8}{2 \times 1.5 \times 10^8} = 1 \, \text{m} = 50 \, \text{cm} \] Step 2: Final Answer.
Thus, the length of the antenna required is 50 cm.