Question

The range of human hearing is roughly from twenty hertz to twentykilohertz. Based on these limits and a value of 305 m/s for the speed of sound, what are thelengths of the longest and shortest pipes (open at both ends andproducing sound at their fundamental frequencies) that you expectto find in a pipe organ?

1 ___________m (shortest pipe)
2 __________m (longest pipe)

Answer 1

1.
`L_s=0.0076\ m`

2.
`L_l=7.62\ m`

Explanation:

Given that

f₁= 20 Hz

f₂= 20 KHz

C= 305 m/s

For open pie organ :

`L=(C)/(2f)`

Shortest length :

`L_s=(C)/(2f_2)`

`L_s=(305)/(2* 20000)`

`L_s=0.0076\ m`

Longest length :

`L_l=(C)/(2f_1)`

`L_l=(305)/(2* 20)`

`L_l=7.62\ m`