Question

The lowest frequency in the audible range is 20 Hz. What are the lengths of (a) the shortest open-open tube and (b) the shortest open-closed tube needed to produce this frequency?

Answer 1

length of the shortest open-open tube 8.6 m

length of the shortest open-closed tube 4.3 m

Step-by-step explanation:

Fundamental frequency for standing wave mode of an open- open tube is given by

`f_(1) =(v)/(2L)`

where v is the velocity of the air ,v=343 m/s and L is the length

The length of open-open tube needed is

`f_(1) =(v)/(2L) \\L=(v)/(2f_(1)) \\L=(343)/(2* 20) \\L=8.6 m`

Fundamental frequency for standing wave mode of an open- close tube is is given by

`f_(1) =(v)/(4L)`

The length of open-close tube needed is

`L=(v)/(4f_(1)) \\L=(343)/(4* 20) \\L=4.3m`