What is the relationship between string tension and frequency on a ukulele?

In summary, the conversation is discussing changes in frequency when the tension of a ukulele string is tightened. The equation PA*V^2 = F is used to calculate the force needed to achieve a certain frequency, and it is assumed that the wavelength remains the same for the fundamental. The equation l=n*lambda/2 is mentioned to support this assumption. The final question asks about the relationship between wavelength and string length.
  • #1
Drizzy
210
1

Homework Statement


You have a ukulele and you change the strings tension so that it becomes tighter. First the frequency was 431 Hz and after we tightened the string the frequency. how much bigger does the force have t be to get that frequency?

Homework Equations



PA*V^2 = F (P = density, A = area)
V=f*lambda

The Attempt at a Solution


F2 = PA V2=PAf22 * lambda2
F1 = PA V2=PAf12 * lambda2
Then i divided F2 by F1 and I got:
f22/f12
which equals to 1,06. My answer is 6 precent bigger.

So my questions are: can I assume that lambda is going to remain the same? Is my solution correct?
 
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  • #2
If lambda here represents the wavelength of the wave in the string, yes you can assume it remains the same. The string length did not change, and we are only interested in the fundamental.
You seem to have omitted the new frequency from the problem statement.
 
  • #3
Sorry, the new frequency is 444Hz. Why can we assume that? That was my initial thought but then I thought wouldn't the wavelength differ if the string is tighter?
 
  • #4
Drizzy said:
Sorry, the new frequency is 444Hz. Why can we assume that? That was my initial thought but then I thought wouldn't the wavelength differ if the string is tighter?
What is the equation relating the wavelength of the nth harmonic to the length of the string?
 
  • #5
it is l=n*lambda/2
 
  • #6
Drizzy said:
it is l=n*lambda/2
Right. So if we are only interested in the fundamental, that fixes n as 1. And the length l of the string does not change. So what does that tell you about lambda?
 

1. How often should I change my guitar strings?

The frequency of changing guitar strings depends on how often you play and the type of strings you use. It is generally recommended to change them every 3-4 months for casual players and every 1-2 months for frequent players.

2. What happens if I don't change my guitar strings?

If you don't change your guitar strings, they will become dull and lose their bright tone. They may also start to rust and break more easily, affecting the overall sound and playability of your guitar.

3. How do I know when it's time to change my guitar strings?

There are a few indicators that it's time to change your guitar strings. These include a noticeable decrease in tone and sustain, visible signs of wear or rust on the strings, and difficulty keeping the guitar in tune.

4. Can I change the tension of my guitar strings?

Yes, you can change the tension of your guitar strings by using different gauges or types of strings. Thicker strings will have higher tension, while thinner strings will have lower tension. However, it's important to note that changing the tension can also affect the playability and sound of your guitar.

5. How do I adjust the tension of my guitar strings?

To adjust the tension of your guitar strings, you can use a truss rod to make small adjustments to the neck of the guitar. However, it's recommended to consult a professional or do thorough research before attempting to adjust the tension yourself, as it can greatly impact the playability and sound of your guitar.

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