The number of `AM` broadcast stations that can be accomodated in a `300kHz` band width for the highest modulating frequency `15 kHz` will be

Options

A. 8
B. 15
C. 10
D. 20

Answer

To solve the problem of how many AM broadcast stations can be accommodated in a 300 kHz bandwidth with a highest modulating frequency of 15 kHz, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship**: The number of AM broadcast stations (N) that can be accommodated in a given bandwidth (B) is related to the highest modulating frequency (f_m) by the formula:
\[ N = \frac{B}{2 \times f_m} \]

2. **Identify the given values**:
- Bandwidth (B) = 300 kHz
- Highest Modulating Frequency (f_m) = 15 kHz

3. **Substitute the values into the formula**:
\[ N = \frac{300 \text{ kHz}}{2 \times 15 \text{ kHz}} \]

4. **Calculate the denominator**:
\[ 2 \times 15 \text{ kHz} = 30 \text{ kHz} \]

5. **Perform the division**:
\[ N = \frac{300 \text{ kHz}}{30 \text{ kHz}} = 10 \]

6. **Conclusion**: The number of AM broadcast stations that can be accommodated is:
\[ N = 10 \]

### Final Answer:
The number of AM broadcast stations that can be accommodated in a 300 kHz bandwidth for the highest modulating frequency of 15 kHz is **10**.

---