1000 kHz carrier wave is amplitude modulated by the signal frequency 200-4000Hz . The channel width of this case is

Options

A. 8 kHz
B. 4 kHz
C. 7.6 kHz
D. 400 kHz

Answer

To solve the problem of finding the channel width for the given amplitude modulated (AM) signal, we can follow these steps:

### Step 1: Identify the Carrier Frequency and Signal Frequency Range
- The carrier frequency (fc) is given as 1000 kHz.
- The signal frequency (fm) varies from 200 Hz to 4000 Hz.

### Step 2: Determine the Maximum Frequency (fm)
- From the given frequency range, the maximum frequency (fm) is 4000 Hz.

### Step 3: Use the Bandwidth Formula for Amplitude Modulation
- The bandwidth (B) for an amplitude modulated wave is given by the formula:
\[ B = 2 \times fm \]
- Here, fm is the maximum frequency of the modulating signal.

### Step 4: Calculate the Bandwidth
- Substitute the maximum frequency into the formula:
\[ B = 2 \times 4000 \text{ Hz} = 8000 \text{ Hz} \]

### Step 5: Convert the Bandwidth to Kilohertz
- Since 1 kHz = 1000 Hz, we convert 8000 Hz to kilohertz:
\[ B = \frac{8000 \text{ Hz}}{1000} = 8 \text{ kHz} \]

### Final Answer
- The channel width for the amplitude modulated signal is **8 kHz**.

---