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

Answer:

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 :

$L=\dfrac{C}{2f}$

Shortest length :

$L_s=\dfrac{C}{2f_2}$

$L_s=\dfrac{305}{2\times 20000}$

$L_s=0.0076\ m$

Longest length :

$L_l=\dfrac{C}{2f_1}$

$L_l=\dfrac{305}{2\times 20}$

$L_l=7.62\ m$