A violin's chord has a length of 0.350 meters, and is tuned to the sound of the note Sol, with a frequency of fG = 392 Hz.
a) How far from the edge of the chord does the violinist need to place his hand, in order to play a note La, with a frequency of fA= 440 Hz?
b) If the accuracy of that position is +- 0.600 cm, which is the maximum alteration of the stress (T)?
fn = n*v/2L = n/2L * sqrt(T/μ)
The Attempt at a Solution
a) From what I gather, and from what my book says about tuning chords, fG is the hamonic. Using that, I can find the speed of the wave in the chord. With n = 1, fG = 392 Hz & L = 0.350 m I get v = 274.4 m/s. So far, so good.
Initially I figured I'd divide fA with fG, find the n and then find the "new" Length, L', and find the difference between that and the initial one, L. Problem is, I don't get an integer result through the division, so I can't go that way.
I looked back to the theory, and it says that you can change the sound of the strings depending on how much you stress them or where you apply it, but it doesn't say anything about whether or not you "tune" it and thus create a "new harmonic" or not.
Since that didn't work, I figure the chord gets tuned again, so I went with fA as the new harmonic, put in n = 1, v =274,4 Hz & looked for L'. That comes out as 0.31. If you findthe difference between that & L, it comes to 4.0 cm, which is different. The book's answer is 3.8 cm.
So, any help? The book's only examples is just one problem of "put numbers in the formula" and it doesn't explain how tuning and whatnot works.
Every bit of assistance is appreciated!