Relating musical notes to vibrations in steel rods(comb)

[yusra347]

Homework Statement

this is a design course project, and I am trying to replicate a music box but with my own choice of music. the concept is the same, a steel comb, being plucked at by protrusions from a rotating cylinder. ok, so the vibrations of each comb tooth are related to the length of the tooth.
i need to know how many teeth i should put in the comb
(There are 13 notes, actually 12, the 13th is the 1st, on a scale, then u go an octave higher and the same notes repeat, that's how any musical instrument works)

Homework Equations

natural frequency of cantelever = [tex]\omega_{n}[/tex] = [tex]\sqrt{k/m}[/tex]
where k= 3EI/[tex]\texts{l^{3}}[/tex] [three E into I over L cubed ]

The Attempt at a Solution

so...i need to know if 12 notes would be enuf for say , something like fur elise? iv heard music boxes play those very shrilly n hardly similar..im not trying to play fur elise though
or do i hav to make a longer piano comb (as i call it) ??
and also the problem being that i have to fabricate this comb :/

 

[Valkarie]

so firstly, i would need to figure out the natural frequency of each tooth. Using the equation given, i would have to calculate the k and m values for the specific material that i am using to fabricate the comb. After that, i would need to determine the length of each tooth. The length of each tooth should be such that the frequency of vibration of each tooth is in tune with the music that i am trying to play. So, depending on the music that i am playing, i would have to adjust the length of the teeth accordingly. Finally, once the length of each tooth is determined, i could calculate the number of teeth required to play the desired music. In general, the number of teeth in the comb would depend on the music that you are trying to play, as well as the material that you are using to fabricate the comb.