Calculating Wave Velocity, Mass, and Wavelength of a Guitar String

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Homework Help Overview

The discussion revolves around calculating wave velocity, mass, and wavelength for a guitar string, specifically focusing on a steel B-string resonating at a fundamental frequency of 240 Hz and a length of 0.680 m. Participants are exploring the relationships between tension, mass, and harmonic wavelengths.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the formula for wave velocity in a stretched string and how to relate tension and mass per unit length. There are attempts to calculate the mass of the string and the wavelength of the third harmonic, with some participants expressing confusion about the calculations involved.

Discussion Status

Some participants have provided calculations for parts of the problem, while others are seeking clarification and assistance. There is a mix of attempts to derive values and questions about the methods used, indicating an ongoing exploration of the concepts involved.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is an emphasis on understanding the relationships between the variables rather than simply arriving at answers.

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Homework Statement


A. A typical steel B-string in a guitar resonates in its fundamental frequency at 240 Hz. The length of the string is 0.680 m. What is the wave velocity in the string?

B. The tension in the above string is 86.8 N. Calculate the mass of a 2 m long piece of the steel string.

C. What is the wavelength of the third harmonic of the guitar string described above?

Homework Equations


f = v/2L
Wavelength = 2L/m

The Attempt at a Solution


A. 326.4
How do I calculate B and C??
 
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B. In stretched string velocity v = sqrt(T/m) where T is the tentsion and m is the mass per unit length of the wire.
CDuring the third harminc the number of loops in the string will be 3.
 
I am sorry but I don't understand how to calculate B still.
 
Does anyone know how to do these?
 
Anyone? I need help :( I'm not figuring this out...
 
v = sqrt(T/m)
326.4 = sqrt(86.8/m). Square both the sides
326.4^2 = 86.8/m
m= 86.8/326.4^2
Mass of 2 m wire = 2m
Now solve.
 
Okay so I get 0.00163 kg...how about part C?
 
I get 834.87 for part C using wavelength = 2L/m
 
I get 834.87 for part C using wavelength = 2L/m

Wave length of third harmonic = 2L/3
 

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