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

Options

A. the size of the required anteena would be at least 5 km which is not convenient.
B. the audio signal cannot 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 understand why an audio signal of 15 kHz frequency cannot be transmitted over long distances without modulation, we can break down the problem step by step:

### Step 1: Understanding the Frequency and Wavelength
The frequency of the audio signal is given as 15 kHz. To understand the transmission characteristics, we first need to calculate the wavelength (λ) of the signal. The relationship between the speed of light (c), frequency (f), and wavelength (λ) is given by the formula:

\[ \lambda = \frac{c}{f} \]

Where:
- \( c \) is the speed of light, approximately \( 3 \times 10^8 \) m/s.
- \( f \) is the frequency, which is \( 15 \times 10^3 \) Hz.

### Step 2: Calculate the Wavelength
Substituting the values into the formula:

\[ \lambda = \frac{3 \times 10^8 \text{ m/s}}{15 \times 10^3 \text{ Hz}} = 20,000 \text{ m} = 20 \text{ km} \]

### Step 3: Determine the Size of the Antenna
The size of the antenna required for effective transmission is typically a fraction of the wavelength. A common rule is that the antenna length should be about \( \frac{\lambda}{4} \):

\[ \text{Antenna Size} = \frac{\lambda}{4} = \frac{20 \text{ km}}{4} = 5 \text{ km} \]

### Step 4: Analyze the Implications
1. **Antenna Size**: The required antenna size of 5 km is impractical for most applications.
2. **Power Radiation**: If the antenna is smaller than the required size, the effective power radiated will be very low, making long-distance transmission ineffective.
3. **Transmission Method**: Audio signals cannot be transmitted via sky waves, which limits the methods of transmission over long distances.

### Conclusion
Thus, an audio signal of 15 kHz cannot be transmitted over long distances without modulation primarily because:
- The size of the required antenna would be at least 5 km, which is not convenient.
- The effective power transmitted would be very low if the size of the antenna is less than 5 km.