If the highest frequency modulating a carrier is 5 kHz, then the number of AM broadcast stations accommodated in a 90 kHz bandwidth are .........

Answer

To solve the problem, we need to determine how many AM broadcast stations can fit within a given bandwidth, given the highest frequency modulating a carrier.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Highest frequency modulating the carrier, \( f_m = 5 \text{ kHz} \)
- Total bandwidth available, \( BW = 90 \text{ kHz} \)

2. **Calculate Bandwidth Required per Station:**
- In Amplitude Modulation (AM), the bandwidth required for each station can be calculated using the formula:
\[ BW_{\text{per station}} = 2 \times f_m \]
- Substituting the value of \( f_m \):
\[ BW_{\text{per station}} = 2 \times 5 \text{ kHz} = 10 \text{ kHz} \]

3. **Calculate the Number of Stations:**
- The number of stations that can be accommodated in the total bandwidth can be calculated as:
\[ \text{Number of Stations} = \frac{BW}{BW_{\text{per station}}} \]
- Substituting the values:
\[ \text{Number of Stations} = \frac{90 \text{ kHz}}{10 \text{ kHz}} = 9 \]

4. **Final Answer:**
- Therefore, the number of AM broadcast stations that can be accommodated in a 90 kHz bandwidth is **9**.