*Question E4D05:
What transmitter frequencies would create an intermodulation-product signal in a receiver tuned to 146.70 MHz when a nearby station transmits on 146.52 MHz?*  

*Correct Answer is  A: 146.34 MHz and 146.61 MHz*  

### AI Response: (may contain errors)  

To determine the transmitter frequencies that would create an intermodulation-product signal in a receiver tuned to 146.70 MHz when a nearby station transmits on 146.52 MHz, we can use the concept of intermodulation products.

### Intermodulation Products
Intermodulation products occur when two signals mix in a non-linear device, such as a receiver. The most common products are generated at frequencies that can be calculated using the following formula:

$$
f_{IM} = |n \cdot f_1 \pm m \cdot f_2|
$$

where:
- $f_{IM}$ = intermodulation frequency
- $f_1$ = frequency of the first signal (146.52 MHz)
- $f_2$ = frequency of the second signal
- $n$ and $m$ are integers (typically 1 or 2 for the first-order products)

### Given Frequencies
- $f_1 = 146.52 \text{ MHz}$
- $f_{receiver} = 146.70 \text{ MHz}$

### Finding the Frequencies
To find the frequencies that would create an intermodulation product at 146.70 MHz, we can set up the equation:

$$
146.70 = |n \cdot 146.52 \pm m \cdot f_2|
$$

For first-order products ($n = 1$, $m = 1$), we can rearrange this to find $f_2$:

1. **Using addition**:
   $$ 
   146.70 = 146.52 + f_2 
   $$
   This gives:
   $$
   f_2 = 146.70 - 146.52 = 0.18 \text{ MHz} \text{ (not a valid frequency)}
   $$

2. **Using subtraction**:
   $$
   146.70 = f_2 - 146.52 
   $$
   This gives:
   $$
   f_2 = 146.70 + 146.52 = 293.22 \text{ MHz} \text{ (not a valid frequency)}
   $$

3. **Using combinations**:
   We can also check combinations of frequencies that are close to the receiver frequency. The correct frequencies can be found by checking the options provided.

### Correct Answer
The correct answer is **A: 146.34 MHz and 146.61 MHz**. 

- **146.34 MHz**: 
  - Using subtraction: 
  $$
  146.70 = 2 \cdot 146.52 - 146.34
  $$
  This is a valid intermodulation product.

- **146.61 MHz**: 
  - Using addition:
  $$
  146.70 = 146.61 + 0.09 \text{ MHz}
  $$
  This is also a valid intermodulation product.

### Why Other Choices Are Incorrect
- **B: 146.88 MHz and 146.34 MHz**: 
  - 146.88 MHz does not produce a valid intermodulation product with 146.52 MHz that results in 146.70 MHz.

- **C: 146.10 MHz and 147.30 MHz**: 
  - Neither of these frequencies produces a valid intermodulation product with 146.52 MHz that results in 146.70 MHz.

- **D: 146.30 MHz and 146.90 MHz**: 
  - Similar to the above, neither frequency produces a valid intermodulation product with 146.52 MHz that results in 146.70 MHz.

### Summary
- The correct frequencies that create an intermodulation product at 146.70 MHz when a nearby station transmits at 146.52 MHz are **146.34 MHz and 146.61 MHz**.
- Understanding how to calculate intermodulation products is crucial for identifying potential interference in amateur radio operations.