The range of human hearing is roughly from twenty hertz to twenty kilohertz. Based on these limits and a value of 360 m/s for the speed of sound, what are the lengths of the longest and shortest pipes (open at both ends and producing sound at their fundamental frequencies) that you expect to find in a pipe organ?

9.0m and 0.009m

Explanation:

Since the hearing capacity range as from low to high. That is from 20Hz to 20000Hz.

F1 = 20Hz and F2 = 20000Hz

Also velocity is given as 360m/s

For the low capacity hearing

V = λf1

360m/s = λ * 20Hz

λ = 360m/s : 20Hz

λ = 18m

Where λ = 2L

18m = 2L

L = 9m

As lo for the high frequency = 20000Hz

V = λf2

360m/s = λ * 20000

λ = 360m/s : 20000

λ = 0.018m

λ = 2L

0.018 = 2L

L = 0.018:2

L = 0.009m

Long length = 9m

Short length = 0.09m

Explanation:

To reach this result, the following calculations are necessary:

Long Length:

360m/s / (2 * 20 Hz) = 9 m

short length:

360m/s / (2 * 20 * 10 ^ 3) = 0.09m