*Question E7E08:
What are the principal frequencies that appear at the output of a mixer?*  

*Correct Answer is  C: The two input frequencies along with their sum and difference frequencies*  

### AI Response: (may contain errors)  

In a mixer, the principal frequencies that appear at the output are derived from the two input frequencies. Let's break down the correct answer and why the other options are incorrect.

### Correct Answer: 
**C: The two input frequencies along with their sum and difference frequencies**

When two signals with frequencies $f_1$ and $f_2$ are mixed, the output will include:
- The original frequencies: $f_1$ and $f_2$
- The sum frequency: $f_1 + f_2$
- The difference frequency: $|f_1 - f_2|$

This is a fundamental property of mixers, often used in radio frequency applications for modulation and demodulation.

### Why the Other Choices are Incorrect:

- **A: Two and four times the input frequency**  
  This option suggests harmonic frequencies, which are not typically produced by a mixer. Mixers generate sum and difference frequencies, not multiples of the input frequencies.

- **B: The square root of the product of input frequencies**  
  This option does not apply to mixers. The square root of the product of frequencies is not a standard output of a mixing process. Mixers do not produce this type of frequency.

- **D: 1.414 and 0.707 times the input frequency**  
  This option refers to specific mathematical constants (the square root of 2 and its reciprocal) but does not relate to the output of a mixer. Mixers do not produce these scaled frequencies.

### Summary:
In summary, when using a mixer, you will always get the two input frequencies, their sum, and their difference. This is crucial for understanding how mixers work in communication systems. 

### Useful Rule of Thumb:
- Remember that mixers are used to combine signals, and the output will always include the original frequencies plus their sum and difference. This is essential for modulation techniques in amateur radio.