In an amplitude modulated wave for audio- frequency of `500 cycle // second`,appropriate carrier frequency will be:

Options

A. `50 cycle//sec`
B. `100cycle//sec`
C. `500 cycle//sec`
D. `50,000 cycle//sec`

Answer

To determine the appropriate carrier frequency for an amplitude modulated wave given an audio frequency of 500 cycles per second, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: In amplitude modulation (AM), the carrier frequency (fc) must always be greater than the audio frequency (f). This is a fundamental principle of AM.

\[ f_c > f \]

2. **Identify the Given Audio Frequency**: The audio frequency provided in the question is 500 cycles per second (Hz).

\[ f = 500 \, \text{Hz} \]

3. **Determine the Minimum Carrier Frequency**: Since the carrier frequency must be greater than the audio frequency, we need to find a frequency that is greater than 500 Hz.

4. **Evaluate the Options**: We will check the provided options to see which one is greater than 500 Hz:
- Option A: 50 Hz (not greater)
- Option B: 100 Hz (not greater)
- Option C: 500 Hz (not greater, must be strictly greater)
- Option D: 50,000 Hz (greater than 500 Hz)

5. **Select the Appropriate Option**: The only option that satisfies the condition \( f_c > 500 \, \text{Hz} \) is:

\[ \text{Option D: } 50,000 \, \text{Hz} \]

### Conclusion:
The appropriate carrier frequency for an audio frequency of 500 cycles per second is **50,000 cycles per second**.

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