If `l_1 and l_2` are the lengths of air column for two air column for two consecutive resonance position when a turning fork of frequency f is sounded in a resonance tube, then end correction is :

Options

A. `((l_2-3l_1))/2`
B. `((l_2+3l_1))/2`
C. `((l_2+l_1))/2`
D. `((3l_2-l_1))/4`

Explanation

To find the end correction when two consecutive resonance positions \( l_1 \) and \( l_2 \) are given, we can follow these steps:

### Step 1: Understanding Resonance in a Tube
When a tuning fork of frequency \( f \) is sounded in a resonance tube, resonance occurs at specific lengths of the air column. The first resonance occurs at a length \( l_1 \) and the second at \( l_2 \).

### Step 2: Establishing the Resonance Conditions
For the first resonance position:
\[
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