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**(1)**My requirement for this project was to build an instrument that can produce all the notes in a C scale. The accuracy of the notes is to be judged through Frequency (Hertz). I decided to build an instrument whose design is comprised of eight electrical conduit tubes (metal) that are about 1.5'' inches in diameter. I strike them with a mallet to produce the sound.

__These are the Frequencies my teacher gave me:__

C - 261.6 Hz

D - 293.7 Hz

E - 329.6 Hz

F - 349.2 Hz

G - 392.0 Hz

A - 440.0 Hz

B - 493.9 Hz

C - 523.3 Hz

**My problem is that I solved for the Length of the eight pieces of tubing (below), but when I went to go test them, the notes that I produced don't seem to be right.**

Together, they definitely do not produce an even scale, and they are not in tune with my piano. If my ear is correct, I believe the notes are all flat. I'll describe the process I went through below. I'd really appreciate any problem-solving advice and suggestions for what could be wrong/how to possibly tune my instrument.

**(2)**These are the equations I used:

__Speed of sound through air:__

v = 331 + (.6*Tc) where Tc = the temperature in Celsius.

__Frequency (Open-Ended Pipe):__

Fn = n * (v/2

**L**) <-- With L being the variable.

Where:

Fn = natural frequency (See the chart above!)

n = 1, 2, 3, etc.

v = speed of sound

L = length of the pipe

**(3)**I used 22 degrees Celsius to solve for the speed of sound, and found that my house was actually at 69 degrees F (20.56 degrees C). I adjusted the house temperature to fit my equation (c. 71 degrees F) and tried again but it didn't help much. I also went back to my Frequency equation to solve with the 20.56 degrees C and saw that it was only the difference of 1 Hz.

Using 22 degrees C, I rearranged the Frequency equation to solve for L. I'm not sure if I did this right, but for the first seven notes of the octave, I treated each note as the natural frequency (so n = 1 for the first notes C - B). I was under the impression I did not need to change n = 2 until I reached the second C of the octave, because that would be the second harmonic. If I'm wrong,

**what do I plug in for n to solve for all the notes?**

So for example:

For C (261.6 Hz):

v = 331 + (.6*Tc)

Tc = 22 degrees C

v = 331 (.6*22)

v = 344.2 m/s

Fn = n * (v/2L)

261.6 Hz = 1 * (344.2/2L)

2L = 344.2/261.6

L = (344.2/261.6)/2

L = 0.657874618 meters

0.657874618 meters --> about 66 cm

I rounded because the guy at Home Depot said he couldn't get much more accurate than that, but that might have been the problem too.

**Would it help to take a few more numbers?**

These are the Lengths (L) that I got using my Frequency equation:

C - 66 cm

D - 58.5 cm

E - 52 cm

F - 49 cm

G - 44 cm

A - 39 cm

B - 35 cm

C - 66 cm

D - 58.5 cm

E - 52 cm

F - 49 cm

G - 44 cm

A - 39 cm

B - 35 cm

**C - 66 cm?**Not sure if this last C note is right! I did the math, and it came out exactly the same, even with n = 2 (because all the 2's cancel out, etc). How do I make this C note an octave higher/lower?

I went and had my lengths of pipe cut, and when I went to play them, they were all off. So, my biggest question is:

**what's causing the notes to be off?**I'm not sure if it's my math, or if I'm using the wrong equation, or if it's something else entirely. Do I need to also account for the speed of sound through the metal tube? If so, how would I do that?

If my idea is an ineffective one for this project, what are some other project suggestions? This project is super important, so I appreciate all the help. Thanks ahead of time! :)

**EDIT:**I went and got a tuner. The notes are really quite awful! I tested the first five notes: C, D, E, F, G and I got

**G sharp (the one below middle C), C, E, F sharp, D (above middle C).**I have no idea what's going on!

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