Determine the greatest length of an organ pipe open at both ends...

The fundamental frequency of an organ pipe open at both ends is given by $f = \dfrac{v}{2L}$, where $v$ is the speed of sound and $L$ is the length of the pipe.

For the length $L$ to be maximum, the fundamental frequency $f$ must be minimum.

The minimum frequency in the normal hearing range is f_{\text\min} = 20 \text{ Hz}.

Substituting the given values, we get L_{\text\max} = \dfrac{v}{2f_{\text\min}}.

L_{\text\max} = \dfrac{340}{2 \times 20} = \dfrac{340}{40} = 8.5 \text{ m}.