You have five tuning forks that oscillate at close but different resonant frequencies. What are the (a) maximum and (b) minimum number of different beat frequencies you can produce by sounding the forks two at a time, depending on how the resonant frequencies differ?

Explanation

To solve the problem, we need to determine the maximum and minimum number of different beat frequencies that can be produced by sounding five tuning forks with different resonant frequencies two at a time.

### Step-by-Step Solution:

1. **Understanding Beat Frequency**:
The beat frequency produced when two tuning forks with frequencies \( f_a \) and \( f_b \) are sounded together is given by \( |f_a - f_b| \).

2. **Calculating Total Pair Combinations**:
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