Question

Two air columns, one open at both ends (A) and one closed at one end (B) have the same fundamental frequency. If the length of column A is 0.74 m, determine the length of column B.

Answer 1

0.37 m

Step-by-step explanation:

The fundamental frequency of an open tube or pipe is

`f_0 = (v)/(2l)`

where v is the velocity of sound and l is the length of the column.

For a closed pipe,

`f_0 = (v)/(4l)`

For column A,

`f_0 = \frac{v}{2*0.74\text{ m}} = \frac{v}{1.48\text{ m}}`

For column B,

`\frac{v}{1.48\text{ m}} = (v)/(4l)`

`4l = 1.48\text{ m}`

`l = 0.37\text{ m}`