An open vertical tube is filled with water and a tuning fork vibrates over the top near the open end. As the water level is lowered in the tube, the first resonance is heard when the water level is at 31 cm from the top of the tube. What is the frequency of the tuning fork? The speed of sound in air is 343 m/s. Answer in units of Hz.

  f = 276.6 Hz

Explanation:

This is a resonance exercise, in this case the fork resonates with the air bale above the water, we can approach this system to an open tube on one side and closed on the other.

At the closed point we have a node and the point fans a maximum or an antinode, so

          L = λ / 4

they indicate that the heard resonance is the fundamental one, so we can reduce the wavelength

          λ = 4 L

          λ = 4   0.31

          λ = 1.24 m

waves have a relationship between their speed and wavelength and frequency

          v = λ f

          f = v /λ

let's calculate

         f = 343 / 1.24

         f = 276.6 Hz

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