In an experiment related to interference , Quinck's tube was employed to determine the speed of sound in air. A tunning fork of frequency `1328 Hz` was used as the sounding source . Initially , the apparatus , yielded a maximum sound intensity . Later , when the slidable tube was drawn by a distance of `12.5 cm`, the intensity was found to be maximum for the first time . Determine the speed of sound in air .

Explanation

To determine the speed of sound in air using the given data from the experiment with Quincke's tube, we can follow these steps:

### Step 1: Understand the Setup
In the experiment, a tuning fork of frequency \( f = 1328 \, \text{Hz} \) is used to produce sound waves. The Quincke's tube is adjusted to create conditions for constructive interference.

### Step 2: Determine the Path Difference
When the tube is drawn out by a distance of \( 12.5 \, \text{cm} \), the path difference between the two sound waves becomes significant. The sound waves traveling through the two paths will have a path difference of:
\[
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