Question

A bandwidth of 6 MHz is available for A.M. transmission. If the maximum audio signal frequency used for modulating the carrier wave is not to exceed 6 kHz. The number of stations that can be broadcasted within this band simultaneously without interfering with each other will be ________.

Hint:

In AM, the signal consists of the carrier and two sidebands (\(f_c + f_m\) and \(f_c - f_m\)), hence the bandwidth is always \(2f_m\).

Answer 1

Correct Answer: 500

Step 1: Understanding the Concept:
In Amplitude Modulation (AM), the bandwidth occupied by a single station is twice the frequency of the modulating audio signal (\( 2 \times f_m \)).
Step 2: Key Formula or Approach:
1. Bandwidth per station = \( 2 \times f_m \).
2. Number of stations = \(\frac{\text{Total Available Bandwidth}}{\text{Bandwidth per station}}\).
Step 3: Detailed Explanation:
Given: Total BW = 6 MHz = \( 6 \times 10^6 \) Hz.
Max audio signal frequency \( f_m = 6 \text{ kHz} = 6 \times 10^3 \) Hz.
BW required per station:
\[ BW_{station} = 2 \times 6 \text{ kHz} = 12 \text{ kHz} = 12 \times 10^3 \text{ Hz} \]
Total number of stations:
\[ N = \frac{6 \times 10^6}{12 \times 10^3} = \frac{6000}{12} = 500 \]
Step 4: Final Answer:
The number of stations is 500.