Answer
The longest possible length of the tube is $8.575~mm$
Work Step by Step
The wavelength of the fundamental frequency of a pipe that is open at both ends is $\lambda = 2L$. We can let $v = 343~m/s$ be the speed of sound in air. We can find the maximum length of the tube:
$\lambda = \frac{v}{f}$
$2L = \frac{v}{f}$
$L = \frac{v}{2f}$
$L = \frac{343~m/s}{(2)(20,000~Hz)}$
$L = 0.008575~m$
$L = 8.575~mm$
The longest possible length of the tube is $8.575~mm$
