Fundamental frequency and tension of a guitar string

In summary, in order to decrease the fundamental frequency of a guitar string by 4%, you need to reduce the tension by .96.
  • #1
BlueSkyy
34
0

Homework Statement



In order to decrease the fundamental frequency of a guitar string by 4%, by what percentage should you reduce the tension?

Homework Equations



f = sqrt [T/(m/L)] / 2L

I believe that is the equation that relates frequency to tension...

The Attempt at a Solution



I plugged in some theoretical values and got 76.96% which seemed wrong, and it is :)
How can I go about solving this problem?
 
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  • #2
[tex] f_1 = (1/(2L)) * \sqrt(F/\mu)[/tex]

Your formula is correct.

First, do f and F vary directly or inversely with each other?
 
  • #3
as L gets bigger, F gets bigger, right?
 
  • #4
Yes, except in this case, they will be getting smaller.

What is the ratio between them?
 
  • #5
if L doubles, than T is quadrupled, right?
 
  • #6
but this has nothing to do with the frequency, since L stays the same...
 
  • #7
Whoops, I misread what you typed. We don't care whether the tension and length vary directly or inversely. We want how frequency and tension are related. The rest of the equation isn't important, since this is just asking for a relative number.

[tex]f \alpha \sqrt(F)[/tex]
 
  • #8
so the frequency is proportional to the square of the tension?
 
  • #9
Yep. So, putting what we know together;
[tex] 0.96f \alpha \sqrt(xF)[/tex]
You need to find x.
 
  • #10
no idea. this is kinda where i got stuck...
 
  • #11
No problem. As [tex]f \alpha \sqrt(F)[/tex], it makes sense that [tex]0.96 \alpha \sqrt(x)[/tex], right? Use [tex] 0.96 = \sqrt(x)[/tex] to solve for x. This will give you a decimal value, which you multiply by 100 to turn into a percent. This is the percent of the original length needed to change the frequency by 4%, so to get the answer, you subtract it from 100%.

% to decrease = 100% - (100x)
 
  • #12
okay, that's what i was thinking, but i didn't know if i could use an equals sign since we were working with a proportion :) thank you!
 
  • #13
Glad to be of help :)
 

1. What is the fundamental frequency of a guitar string?

The fundamental frequency of a guitar string is the lowest and most prominent frequency produced by the string when it is plucked or strummed.

2. How is the fundamental frequency of a guitar string determined?

The fundamental frequency of a guitar string is determined by several factors, including the length, mass, and tension of the string. The longer the string, the lower the frequency. The heavier the string, the lower the frequency. And the higher the tension, the higher the frequency.

3. What is the relationship between tension and frequency of a guitar string?

The tension of a guitar string is directly proportional to its frequency. This means that as the tension of the string increases, its frequency also increases. Conversely, as the tension decreases, the frequency decreases as well.

4. How does changing the tension of a guitar string affect its sound?

Changing the tension of a guitar string can greatly affect its sound. Increasing the tension will result in a higher frequency and a brighter, more crisp sound. Decreasing the tension will result in a lower frequency and a warmer, more mellow sound.

5. Can the fundamental frequency of a guitar string be changed?

Yes, the fundamental frequency of a guitar string can be changed by altering its length, mass, or tension. This is often done through tuning the guitar, which involves adjusting the tension of each string to produce the desired frequency for each note.

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