Musical Instrument Project: Frequencies Aren't Right?
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.
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/2L) <-- 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
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?
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! :)
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.
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/2L) <-- 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
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?
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! :)