A \(40-\mathrm{cm}-\) long tube has a \(40-\mathrm{cm}-\) long insert that can be pulled in and out, as shown in Figure P16.59. A vibrating tuning fork is held next to the tube. As the insert is slowly pulled out, the sound from the tuning fork creates standing waves in the tube when the total length \(L\) is \(42.5 \mathrm{~cm}, 56.7 \mathrm{~cm}\), and \(70.9 \mathrm{~cm}\). What is the frequency of the tuning fork? The air temperature is \(20^{\circ} \mathrm{C}\).

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40 cm 40 cm L FIGURE P16.59