Physics Help?

Question

I have this question on my Physics HW and I am having a little trouble. I think I may be making it more complicated than it is. Here is the question
A violin string vibrates at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one third of the way down from the end?

I am not seeing how where I "finger" the string is going to affect it. It doesn't seem to be explaining this in my book and I am taking this online. You don't have to give me the answer but some guidance on solving it would be great. Thanks in advance.

Answer 1

The choice of the violin was a bit unfortunate since violins have a special frequency response that is not a parabolic wave when properly bowed:
http://plus.maths.org/issue31/features/woodhouse/

Well, that may not be the point here since the author of the book probably assumed that the string follows the harmonic frequency behavior as described by:

f=sqrt(T/u)/(2*L)
where T is the tension
u is the linear mass (Mass per unit length)
L is the length
And f is the frequency harmonic.

The act of "fingering" the string is to depress it and thereby change the length. You can likely assume that this has negligible effect on the tension of the string. So if when fingered the new l = 2L/3
you just plug that into the equation and solve using a ratio:

f=K/L
f'=3K/2L
f"/f=3/2

j

Answer 2

lets say that 294 Hz gives us a C note with no strings depressed. if we go half way down the neck and play the string the pitch would be twice as high, no?

Answer 3

ok with guitar or any stringed instrument when you finger it you make less string that vibrates. So the Sound gets higher pitched as you go down the neck