Question

The range of human hearing is roughly from twenty hertz to twenty kilohertz. Based on these limits and a value of 343 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?

Answer 1

Explanation:

It is given that, the range of human hearing is roughly from twenty hertz to twenty kilohertz.

Minimum frequency, f = 20 Hz

Maximum frequency, f' = 20,000 Hz

We need to find the lengths of the longest and shortest pipes. For open pipes, the length of pipe is given by :

$l=\dfrac{v}{2f}$

For shortest pipe, frequency should be maximum, $l=\dfrac{343\ m/s}{2\times 20000\ Hz}$

l = 0.008575 m

For longest pipe, frequency should be minimum, $l'=\dfrac{343\ m/s}{2\times 20\ Hz}$

l' = 8.575 m

So, the lengths of longest and shortest pipes are 8.575 meters and 0.008575 meters respectively.