Bandwidth available, BW = 6 MHz
Maximum audio frequency, \(f_{max}\) = 5 KHz
Number of AM broadcast stations that can be accommodated, \(N = \)?
Solution:
The total number of AM broadcast stations that can be accommodated in the given bandwidth can be calculated using the formula:
$$N = \frac{\text{Total bandwidth available}}{\text{Bandwidth required for each station}}$$
The bandwidth required for each station can be calculated as:
$$BW_{required} = 2 \times (f_{max} + 5 KHz)$$
Where,
\(f_{max}\) = Maximum audio frequency
5 kHz = Guard band
Substituting the given values, we get:
$$BW_{required} = 2 \times (5 \text{ KHz} + 5 \text{ KHz}) = 20 \text{ KHz}$$
Now, we can calculate the total number of stations:
$$N = \frac{\text{Total bandwidth available}}{\text{Bandwidth required for each station}} = \frac{6 \text{ MHz}}{20 \text{ KHz}} = \frac{6000 \text{ KHz}}{20 \text{ KHz}} = 300$$
Therefore, the given bandwidth of 6 MHz can accommodate 300 AM broadcast stations, each transmitting an audio signal with a maximum frequency of 5 kHz and a guard band of 5 kHz.