A band width of 5 MHz is available for AM transmission. If the maximum audio signal frequency used for modulating the carrier is not to exceed 5 kHz, how many stations can be broad cast within this band simultaneously without interfering with eachother?

Options

A. 200
B. 300
C. 400
D. 500

Explanation

To solve the problem, we need to determine how many AM stations can be broadcast simultaneously within a bandwidth of 5 MHz, given that the maximum audio signal frequency for modulation is 5 kHz.

### Step-by-Step Solution:

1. **Understand the Bandwidth Requirement for AM Transmission:**
The bandwidth (BW) required for each AM station can be calculated using the formula:
\[ \text{Bandwidth} = 2 \times \text{Maximum Audio Frequency} \]
Here, the maximum audio frequency is given as 5 kHz.

2. **Calculate the Bandwidth for One Station:**
Substituting the maximum audio frequency into the formula:
\[ \text{Bandwidth} = 2 \times 5 \text{ kHz} = 10 \text{ kHz} \]

3. **Convert the Total Bandwidth Available to the Same Units:**
The total bandwidth available for AM transmission is given as 5 MHz. We need to convert this into kilohertz (kHz) for consistency:
\[ 5 \text{ MHz} = 5000 \text{ kHz} \]

4. **Calculate the Number of Stations:**
To find the number of stations that can be accommodated within the available bandwidth, we divide the total bandwidth by the bandwidth required for one station:
\[ \text{Number of Stations} = \frac{\text{Total Bandwidth}}{\text{Bandwidth per Station}} = \frac{5000 \text{ kHz}}{10 \text{ kHz}} = 500 \]

5. **Conclusion:**
Thus, the maximum number of AM stations that can be broadcast simultaneously without interfering with each other is **500**.