A bandwidth of 10 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 broadcasted within this band simultaneously without interfering with each other ?

Answer

To solve the problem, we need to determine how many AM stations can be broadcasted simultaneously within a given bandwidth without interfering with each other.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Available bandwidth (BW) = 10 MHz = \(10 \times 10^6\) Hz
- Maximum audio signal frequency (fm) = 5 kHz = \(5 \times 10^3\) Hz

2. **Calculate the Bandwidth Required for Each Station:**
- The bandwidth for each AM station is determined by the formula:
\[ BW_{station} = 2 \times f_m \]
- Substituting the value of \(f_m\):
\[ BW_{station} = 2 \times (5 \times 10^3) = 10 \times 10^3 \text{ Hz} = 10 \text{ kHz} \]

3. **Calculate the Number of Stations:**
- The number of stations that can be accommodated within the available bandwidth is given by:
\[ \text{Number of Stations} = \frac{BW_{available}}{BW_{station}} \]
- Substituting the values:
\[ \text{Number of Stations} = \frac{10 \times 10^6 \text{ Hz}}{10 \times 10^3 \text{ Hz}} = \frac{10^7}{10^4} = 10^3 = 1000 \]

4. **Final Answer:**
- Therefore, the number of AM stations that can be broadcasted simultaneously without interfering with each other is **1000**.