The lowest frequency in the audible range is 20 hz. a)what is the length of the shortest open-open tube needed to produce this frequency? b)what is the length of the shortest open-closed tube needed to produce this frequency?

a) 8.58 m

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

where

f is the fundamental frequency (the lowest frequency)

v is the speed of sound

L is the length of the tube

In this problem, we have

f = 20 Hz

v = 343 m/s (speed of sound in air)

Solving the equation for L, we find the shortest length of the tube:

(b) 4.29 m

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

Where in this problem, we have

f = 20 Hz

v = 343 m/s (speed of sound in air)

Solving the equation for L, we find the shortest length of the tube:

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