Question

An organ pipe is made to play a low note at 27.5 Hz, the same as the lowest note on a piano. Assuming a sound speed of 343 m/s, what length open-open pipe is needed? What length open-closed pipe would suffice?

Answer 1

Answer:

The length of open-open pipe needed is 6.23 m

The length of open-close  pipe needed is 3.11 m

Explanation:

Fundamental frequency for standing wave mode of  an open- open pipe is given by

$f=\frac{v}{2L}$

where v is the velocity and L is the length

The length of open-open pipe needed is

$L=\frac{v}{2f} \\L=\frac{343}{2\times 27.5} \\L=6.23 m$

Fundamental frequency for standing wave mode of  an open- close pipe is given by

$f=\frac{v}{2L}$

The length of open-close pipe needed is

$L=\frac{v}{2f} \\L=\frac{343}{2\times 27.5} \\L=6.23 m$