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 step by step, we will calculate the number of AM stations that can be broadcast simultaneously within a given bandwidth without interference.

### Step 1: Understand the given data
- Total available bandwidth for AM transmission = 5 MHz
- Maximum audio signal frequency for modulation = 5 kHz

### Step 2: Calculate the bandwidth required for each station
For AM transmission, the bandwidth (BW) required for each station is given by the formula:
\[ \text{BW} = 2 \times f_m \]
where \( f_m \) is the maximum audio signal frequency.

Substituting the given value:
\[ \text{BW} = 2 \times 5 \text{ kHz} = 10 \text{ kHz} \]

### Step 3: Convert the total bandwidth into the same units
The total available bandwidth is given in MHz. We need to convert it into kHz for consistency:
\[ 5 \text{ MHz} = 5 \times 10^3 \text{ kHz} = 5000 \text{ kHz} \]

### Step 4: Calculate the number of stations that can be broadcast
To find the number of stations (\( N \)) that can be broadcast simultaneously, we use the formula:
\[ N = \frac{\text{Total Bandwidth}}{\text{Bandwidth of each station}} \]

Substituting the values:
\[ N = \frac{5000 \text{ kHz}}{10 \text{ kHz}} = 500 \]

### Step 5: Conclusion
The total number of AM stations that can be broadcast simultaneously without interfering with each other is **500**.