This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

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Answer
340 , \text{Hz}$
To solve this problem, we need to find the wavelength of the sound produced by the tuning fork and then determine the possible lengths of the air column that will cause resonance in the closed-end tube. Finally, we'll calculate the corresponding water heights and find the minimum among them.
Given:
Step 1: Calculate the wavelength () of the sound wave. The relationship between the speed of sound (), frequency (), and wavelength ($\lambda
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Finally, we'll calculate the corresponding water heights and find the minimum among them.
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.