A set of 24 tuming forka is arranged in series of Locrening frequencies. If each tuning fork gives 4 beats/sec with the preceding one and the last fork is found to be the octave of the first, calculate the frequences of the first and the last.

Explanation

To solve the problem, we need to find the frequencies of the first and the last tuning fork in a series of 24 tuning forks arranged in increasing frequencies, where each fork produces 4 beats per second with the preceding one, and the last fork is an octave of the first.

### Step-by-Step Solution:

1. **Define the Variables:**
Let the frequency of the first tuning fork be \( f \). Since the last fork is an octave of the first, its frequency will be \( 2f \).

2. **Understanding Beats:**
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