The LA Philharmonic has a giant new organ in its new Disney Concert Hall which w

Question

The LA Philharmonic has a giant new organ in its new Disney Concert Hall which was designed by Frank Gehry. The pipes look like a McDonald's fry pack. For the questions below, assume that the speed of sound is 337 m/s.
(a) The highest frequency the pipe organ can sound is 10548 Hz. If the pipe which sounds this pitch is open on both ends what is its length in cm?
cm

(b) How long would the 10548 Hz pipe be if it was closed on one end?
cm

(c) The lowest frequency pipes of the organ are only 16 Hz which is the note C which is below the lowest key on a grand piano. If the pipe which sounds this note is open on both ends what is its length?
m

(d) How long would a 16 Hz organ pipe be if it was closed on one end?
m

Explanation / Answer

(a) because the pipe is open at both ends the following relatioship will be:
=2L

now we can say:

v=f

v=2fL

L=v/(2f)

L=337/(2*10548)

L=1.597 cm

(b) now that the pipe is closed on one side the relationship is:

=4L

now we can say:

v=f

v=4fL

L=v/(4f)

L=337/(4*10548)

L=0.799 cm

(c)

because the pipe is open at both ends the following relatioship will be:
=2L

now we can say:

v=f

v=2fL

L=v/(2f)

L=337/(2*16)

L=10.53 m

(d) now that the pipe is closed on one side the relationship is:

=4L

now we can say:

v=f

v=4fL

L=v/(4f)

L=337/(4*16)

L=5.27 m

hope that helps

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