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 of how many AM stations can be broadcasted simultaneously within a bandwidth of 10 MHz, we can follow these steps:

### Step 1: Understand the Given Information
We are provided with:
- Total available bandwidth for AM transmission = 10 MHz
- Maximum audio signal frequency (FM) used for modulating the carrier = 5 kHz

### Step 2: Calculate the Bandwidth Required for One Station
The bandwidth (BW) required for one AM station can be calculated using the formula:
\[ \text{BW} = 2 \times FM \]
Substituting the given value of FM:
\[ \text{BW} = 2 \times 5 \text{ kHz} = 10 \text{ kHz} \]

### Step 3: Convert Units for Consistency
To ensure consistency in our calculations, we convert the total bandwidth from MHz to kHz:
\[ 10 \text{ MHz} = 10 \times 10^3 \text{ kHz} = 10,000 \text{ kHz} \]

### Step 4: Calculate the Number of Stations
Now, we can find the number of stations (N) that can be accommodated within the total bandwidth by dividing the total bandwidth by the bandwidth required for one station:
\[ N = \frac{\text{Total Bandwidth}}{\text{Bandwidth of One Station}} \]
Substituting the values:
\[ N = \frac{10,000 \text{ kHz}}{10 \text{ kHz}} = 1,000 \]

### Step 5: Conclusion
Thus, the number of AM stations that can be broadcasted simultaneously without interfering with each other is:
\[ \boxed{1000} \]

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