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

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Homework Help Overview

The discussion revolves around the relationship between string tension and frequency in the context of a ukulele. The original poster examines how tightening the strings affects the frequency, initially at 431 Hz and later at 444 Hz, while exploring the implications of these changes on the wavelength.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to relate changes in frequency to changes in tension using equations involving density, area, and wave properties. They question whether the wavelength remains constant despite changes in tension. Other participants clarify the relationship between wavelength and string length, particularly for the fundamental frequency.

Discussion Status

Participants are actively engaging with the problem, providing clarifications and posing questions about assumptions regarding wavelength and frequency. Some guidance has been offered regarding the relationship between string length and wavelength for the fundamental frequency, but no consensus has been reached on the implications of tension changes.

Contextual Notes

The discussion includes a focus on the fundamental frequency and its relationship to string length, with participants questioning the assumptions made about wavelength in the context of changing tension. The original poster's omission of the new frequency was noted, prompting further exploration of the problem.

Drizzy
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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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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.
 
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?
 
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?
 
it is l=n*lambda/2
 
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?
 

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