If a carrier wave of 1000 kHz is used to carry the signal, the length of transmitting antenna will be equal to -

Options

A. 3 m
B. 30 m
C. 75 m
D. 3000 m

Answer

To find the length of the transmitting antenna when a carrier wave of 1000 kHz is used, we can follow these steps:

### Step 1: Convert the frequency to SI units
The frequency given is 1000 kHz. We need to convert this into Hertz (Hz).
\[ \text{Frequency} (f) = 1000 \, \text{kHz} = 1000 \times 10^3 \, \text{Hz} = 10^6 \, \text{Hz} \]

### Step 2: Calculate the wavelength (λ)
The wavelength (λ) can be calculated using the formula:
\[ \lambda = \frac{c}{f} \]
where \(c\) is the speed of light, approximately \(3 \times 10^8 \, \text{m/s}\).

Substituting the values:
\[ \lambda = \frac{3 \times 10^8 \, \text{m/s}}{10^6 \, \text{Hz}} = 300 \, \text{m} \]

### Step 3: Calculate the length of the transmitting antenna (L)
The length of the transmitting antenna is given by:
\[ L = \frac{\lambda}{4} \]
Substituting the value of λ we found:
\[ L = \frac{300 \, \text{m}}{4} = 75 \, \text{m} \]

### Conclusion
The length of the transmitting antenna will be **75 meters**.

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