Question

What is the length of the shortest open-closed tube needed to produce this frequency?

Answer 1

The whole question is;
The lowest frequency in the audible range is 20Hz.
What is the length of the shortest open-closed tube needed to produce this frequency?
The fundamental resonant frequency of the tube opened at one end is given by this formula:

`f_1=(v_s)/(4L)`
Where v_s is the speed of sound in the air, and L is the length of the tube.
The speed of sound at 20 degrees Celsius is v_s=343.7m/s.
So the shortest length is:

`f_1=(v_s)/(4L)\\ L=(v_s)/(4f_1)\\ L=(343.7)/(4\cdot 20)=4.29m`