Length of string on instrument to produce specific frequency

  • Thread starter idkididk
  • Start date
  • #1
5
0

Homework Statement


You are designing a two-string instrument with metal string 35.0 long, as shown in the figure . Both strings are under the same tension. String has a mass of 8.45 and produces the note middle C (frequency 262 ) in its fundamental mode.

To extend the range of your instrument, you include a fret located just under the strings, but not normally touching them. How far from the upper end should you put this fret so that when you press tightly against it, this string will produce C# (frequency 277 ) in its fundamental?

Homework Equations



f= (1/(2L)) * (F/u)^.5, where f is the frequency, L is length of the string, u is the mass per unit distance, and F is the tension force.

The Attempt at a Solution



So I found that the tension of the string to be 812N. Using that, I solved for x: 277= (1/(2x)) *(812/(.00845/x))^.5

x= .313, which means 31.3 cm. It's asking how far form the upper end, so 35-31.3cm = 3.7cm.

However, this is not correct. Anyone know why?
 

Answers and Replies

  • #2
Doc Al
Mentor
44,987
1,259
So I found that the tension of the string to be 812N.
How did you solve for that? What units are the length and mass given in?

Edit: I see. Length in cm and mass in grams.
 
  • #3
Doc Al
Mentor
44,987
1,259
So I found that the tension of the string to be 812N. Using that, I solved for x: 277= (1/(2x)) *(812/(.00845/x))^.5
8.45 is the mass of the full string, so don't divide by the new (smaller) length to find μ. (μ is a constant for the string material, regardless of length.)
 
  • #4
5
0
^I just tried that, 277= (1/(2x)) *(812/(.00845/.35))^.5, and got x=33cm, so the answer would be 2, but that's not it either

EDIT: Ok nevermind the answer is 1.9 lol. Thanks!
 
Last edited:

Related Threads on Length of string on instrument to produce specific frequency

Replies
2
Views
2K
Replies
3
Views
2K
Replies
2
Views
2K
Replies
32
Views
3K
Replies
1
Views
626
  • Last Post
Replies
8
Views
1K
Replies
16
Views
4K
Replies
1
Views
419
Replies
10
Views
9K
Top