**1. 8.5 m**

For an open-open tube, the frequency of the fundamental mode of vibration is given by

where

v is the speed of the sound wave

L is the length of the tube

In this problem, we have:

f = 20 Hz is the frequency of the fundamental mode

v = 340 m/s is the speed of sound in air

Re-arranging the equation, we find

**2. 4.25 m**

For an open-closed tube instead, the frequency of the fundamental mode of vibration is given by

where

v is the speed of the sound wave

L is the length of the tube

In this problem, we have:

f = 20 Hz is the frequency of the fundamental mode

v = 340 m/s is the speed of sound in air

Re-arranging the equation, we find