An audio signal of 15 kHz frequency cannot be transmitted over long distance without modulation because.

Options

A. the size of the required antenna would be at least 5 km which is not convenient
B. the audio signal can not be transmitted through sky waves
C. the size of the required antenna would be at least 20 km, which is not convenient
D. effective power transmitted would be very low, if the size of the antenna is less than 5 km

Explanation

To solve the question regarding why an audio signal of 15 kHz frequency cannot be transmitted over long distances without modulation, we will analyze the options provided and the underlying physics principles.

### Step-by-Step Solution:

1. **Identify the Frequency**:
The frequency of the audio signal is given as 15 kHz. This can be converted to Hertz:
\[ f = 15 \text{ kHz} = 15 \times 10^3 \text{ Hz} \]

2. **Calculate the Wavelength**:
The wavelength (\(\lambda\)) of a wave can be calculated using the formula:
\[ \lambda = \frac{c}{f} \]
where \(c\) is the speed of light (\(3 \times 10^8 \text{ m/s}\)). Substituting the values:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{15 \times 10^3 \text{ Hz}} = \frac{3 \times 10^8}{15 \times 10^3} = \frac{3}{15} \times 10^5 = \frac{1}{5} \times 10^5 \text{ m} = 2 \times 10^4 \text{ m} = 20 \text{ km} \]

3. **Determine the Required Antenna Size**:
The size of the antenna required for transmission is typically taken as \(\frac{\lambda}{4}\):
\[ L = \frac{\lambda}{4} = \frac{20 \text{ km}}{4} = 5 \text{ km} \]

4. **Analyze the Implications**:
- **Antenna Size**: The calculated antenna size is 5 km, which is quite large and not convenient for practical use.
- **Transmission Limitations**: Audio signals, being low-frequency waves, cannot be transmitted effectively over long distances without modulation. They cannot utilize sky waves for long-distance transmission due to atmospheric absorption.

5. **Evaluate the Options**:
- **Option 1**: The size of the required antenna would be at least 5 km, which is correct.
- **Option 2**: The audio signal cannot be transmitted through sky waves, which is also correct.
- **Option 3**: The size of the required antenna would be at least 20 km, which is incorrect as we calculated it to be 5 km.
- **Option 4**: The effective power transmitted would be very low if the size of the antenna is less than 5 km, which is correct.

### Conclusion:
The correct answers are Option 1, Option 2, and Option 4.