Height of antenna of transmitter and receiver is proportional to:

Options

A. frequency of carier wave
B. `(1)/("modulation frequency")`
C. both
D. none of these

Answer

To solve the question regarding the proportionality of the height of antennas of transmitters and receivers, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Antenna Height**:
The height of antennas for transmitters and receivers is an important factor in communication systems. It is influenced by various parameters, including the wavelength of the signal being transmitted.

2. **Maxwell's Equations and Antenna Theory**:
According to electromagnetic theory, particularly Maxwell's equations, the effective height of an antenna is related to the wavelength of the signal. The maximum power transfer theorem indicates that antennas should be designed with specific height ratios to optimize signal transmission.

3. **Height Proportional to Wavelength**:
The height of the antenna is typically proportional to the wavelength of the signal. For practical antennas, common heights are often expressed as fractions of the wavelength (e.g., λ/4, λ/2, etc.).

4. **Wavelength and Frequency Relationship**:
Wavelength (λ) is inversely related to frequency (f) through the equation:
\[ c = f \cdot \lambda \]
where \(c\) is the speed of light. This implies that as frequency increases, the wavelength decreases.

5. **Conclusion**:
Since the height of the antenna is proportional to the wavelength, and the wavelength is inversely proportional to the frequency, we can conclude that the height of the antenna is inversely proportional to the frequency of the signal.

### Final Answer:
The height of the antenna of the transmitter and receiver is proportional to \( \frac{1}{f} \) (where \( f \) is the modulation frequency).