A 70 kHz bandwidth is to accommodate 7 AM broadcast signals simultaneo...
To accommodate 7 AM broadcast signals simultaneously within a bandwidth of 70 kHz, we need to determine the maximum modulation frequency that each station must be limited to. Let's break down the problem step by step.
1. Define the bandwidth:
The total bandwidth available is 70 kHz, which includes both the signals and a guard band of 5 kHz. Therefore, the usable bandwidth for the signals is 70 kHz - 5 kHz = 65 kHz.
2. Determine the bandwidth per station:
To accommodate 7 stations within the usable bandwidth, we need to divide the bandwidth equally among them. Thus, the bandwidth per station is 65 kHz / 7 = 9.2857 kHz.
3. Account for modulation:
In amplitude modulation (AM), the bandwidth required is twice the maximum modulation frequency. Let's denote the maximum modulation frequency as f_m. So, the bandwidth required per station is 2f_m.
4. Calculate the maximum modulation frequency:
The bandwidth per station is 9.2857 kHz, which is equal to 2f_m. Solving for f_m, we get f_m = 9.2857 kHz / 2 = 4.6429 kHz.
5. Account for the guard band:
Since a guard band of 5 kHz is present, we need to subtract this from the maximum modulation frequency to ensure that the signals do not overlap. Therefore, the maximum modulation frequency each station should be limited to is f_m - 5 kHz = 4.6429 kHz - 5 kHz = -0.3571 kHz.
Note: The negative value indicates that there is no room for each station to transmit at the maximum modulation frequency. As a result, the maximum modulation frequency each station must be limited to is 0.3571 kHz.
Therefore, the correct answer is option C) 2.85 kHz.