What is the Tension of a Cello String with Given Frequency and Linear Density?

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Homework Help Overview

The discussion revolves around calculating the tension of a cello string given its linear density, frequency, and length. The subject area includes concepts from wave mechanics and string vibrations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to find the velocity of the wave on the string before calculating tension, but questions the use of the string length in relation to wavelength. Some participants clarify the relationship between string length and wavelength in the fundamental mode.

Discussion Status

The discussion is progressing with clarifications being provided about the relationship between string length and wavelength. Participants are engaging with the concepts and correcting misunderstandings without reaching a final conclusion.

Contextual Notes

The original poster is working within the constraints of a homework assignment, which may limit the information they can use or the methods they can apply.

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Homework Statement



On a cello, the string has (linear density) m/L = 1.56 x 10^-2 kg/m, and produces frequency of 65.4 Hz and has length of .800 m between the fixed ends. Find the tension.

Homework Equations



v= sqrt(F/(m/L))

v= f (lambda)

The Attempt at a Solution



I first thought to find the velocity first, then plug in the velocity into the first equation and then find the tension. But, then I figured that the length given was the length of the string and not the wavelength so that eliminates using the second equation. Is there another equation to use, that's not occurring to me to find the velocity?
 
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Your equatoins are correct, but the length of the string is half the wavelength for the fundamental mode, so λ = 2L.
 
thanks dx that clears up a lot
 
No problem. Welcome to PF.
 

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