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

Options

A. 50 cycles/s
B. 100 cycles/s
C. 500 cycles/s
D. 50,000 cycles/s

Answer

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

### Step-by-Step Solution:

1. **Identify the Modulating Frequency**:
- The modulating frequency (fm) is given as 500 cycles/second, which is equivalent to 500 Hz.

2. **Understand the Relationship Between Carrier Frequency and Modulating Frequency**:
- In amplitude modulation, the carrier frequency (fc) must be greater than the modulating frequency (fm). This is a fundamental requirement for effective modulation.

3. **State the Condition**:
- The condition can be expressed mathematically as:
\[ f_c > f_m \]
- Substituting the known value:
\[ f_c > 500 \text{ Hz} \]

4. **Choose an Appropriate Carrier Frequency**:
- We need to select a carrier frequency that is significantly higher than 500 Hz. Common practice is to choose a carrier frequency that is at least 10 times higher than the modulating frequency for effective modulation.
- Therefore, a suitable carrier frequency could be:
\[ f_c = 5000 \text{ Hz} \text{ or higher} \]
- However, in the options provided, if we have a choice of 50000 Hz, that would be a suitable carrier frequency.

5. **Conclusion**:
- The appropriate carrier frequency for an audio frequency of 500 Hz is 50000 Hz.

### Final Answer:
The appropriate carrier frequency for an audio frequency of 500 cycles/second is **50000 Hz**.