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 least 5 km which is not conveient.
B. the audio signal can not be trasmitted through sky waves.
C. effective power transmitted would be very low. If the size of the antenna is less than 5 km.
D. all of these

Answer

To understand why an audio signal of 15 kHz frequency cannot be transmitted over long distances without modulation, we can break down the explanation into several steps:

### Step-by-Step Solution:

1. **Understanding the Frequency**:
- The given audio signal has a frequency of 15 kHz, which is equal to \( 15 \times 10^3 \) Hz.

2. **Calculating the Wavelength**:
- The wavelength (\( \lambda \)) of a signal can be calculated using the formula:
\[ \lambda = \frac{c}{\nu} \]
where \( c \) is the speed of light (\( 3 \times 10^8 \) m/s) and \( \nu \) is the frequency.
- Substituting the values:
\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{15 \times 10^3 \text{ Hz}} = 20000 \text{ m} = 0.2 \times 10^5 \text{ m} \]

3. **Determining Antenna Size**:
- The size of the antenna required for effective transmission is given by:
\[ h = \frac{\lambda}{4} \]
- Substituting the calculated wavelength:
\[ h = \frac{0.2 \times 10^5 \text{ m}}{4} = 5000 \text{ m} = 5 \text{ km} \]

4. **Understanding the Implications**:
- An antenna size of 5 km is impractical for most applications. This large size is required to effectively transmit the low-frequency audio signal over long distances.

5. **Conclusion**:
- Due to the impracticality of constructing a 5 km antenna, audio signals of low frequency (like 15 kHz) cannot be transmitted over long distances without modulation. Modulation allows the signal to be superimposed on a higher frequency carrier wave, which can be transmitted more effectively.