The length of the antenna required for the transmission of frequencies of em waves of band width having AF range is

Options

A. 15 km
B. 1500 m
C. 300 m
D. 3.75km

Answer

To find the length of the antenna required for the transmission of electromagnetic waves in the audio frequency range, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Maximum Audio Frequency**:
The maximum audio frequency that humans can hear is approximately 20,000 Hz (20 kHz).

2. **Understand the Relationship Between Antenna Length and Wavelength**:
The length of the antenna is typically taken as one-fourth of the wavelength (λ) of the electromagnetic wave. This can be expressed as:
\[ L = \frac{1}{4} \lambda \]

3. **Calculate Wavelength (λ)**:
The wavelength can be calculated using the formula:
\[ \lambda = \frac{C}{f} \]
where \( C \) is the speed of light (approximately \( 3 \times 10^8 \) m/s) and \( f \) is the frequency in Hz.

4. **Substitute the Values**:
Substituting the values into the wavelength formula:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{20000 \text{ Hz}} = \frac{3 \times 10^8}{2 \times 10^4} = 15000 \text{ m} \]

5. **Calculate the Length of the Antenna**:
Now, substituting the wavelength back into the antenna length formula:
\[ L = \frac{1}{4} \lambda = \frac{1}{4} \times 15000 \text{ m} = 3750 \text{ m} \]

6. **Convert to Kilometers**:
Since the question may require the answer in kilometers, we convert meters to kilometers:
\[ L = 3750 \text{ m} = 3.75 \text{ km} \]

### Final Answer:
The length of the antenna required for the transmission of frequencies of electromagnetic waves of bandwidth having an audio frequency range is **3.75 kilometers**.