Standing Waves on a Violin String

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Homework Help Overview

The discussion revolves around the physics of standing waves on a violin string, specifically focusing on the relationship between string length, tension, frequency, and wavelength in the context of sound production in stringed instruments.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the calculation of string tension and frequency, questioning the assumptions regarding the fundamental frequency and the distinction between wave speeds in the string and air. Some participants express uncertainty about the appropriateness of using the fundamental frequency in this context.

Discussion Status

There is ongoing exploration of the relationships between frequency, wavelength, and tension. Some participants have provided calculations and insights, while others are questioning the assumptions made about the fundamental frequency and the velocities involved.

Contextual Notes

Participants are navigating the complexities of wave mechanics in different media, with specific attention to the assumptions made in the problem statement regarding the fundamental frequency and the properties of sound in air versus the string.

kikko
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Homework Statement



A violinist places her finger so that the vibrating section of a 1.00 g/m string has a length of 40.0 cm, then she draws her bow across it. A listener nearby in a 20oC room hears a note with a wavelength of 60.0 cm.

Homework Equations



Wavelengthm = (2L/m)
f1 = (v/2L) = (1/2L)(sqrt(Ts/(m/L)

The Attempt at a Solution

(((2Lf)^2)M)/LWhat am I doing something wrong?
 
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what are you trying to find, string tension?

I think you should find frequency using speed of sound and wavelength

you've assumed the frequency to be the fundamental frequency which I don't think is right...besides that I think there should also be some distinction between the speed of the wave traveling through the guitar string medium and the speed of sound through air, but I'm not too sure...
 
The book says to always use the fundamental frequency for stringed instruments, and from the text so far i really doubt it changes between the string and the air. Yes,I am trying to find string tension.
 
ok here's what I got

fundamental wavelength = 0.8
f=343/0.6 = 572 Hz

T/0.001 = (0.8 x 572)^2
T=209N

there is a distinction between velocity through air and the string, but the fundamental frequency as you said remains the same, thus we can use the speed of sound to find the fundamental frequency, multiply this by the wavelength on the string, and voila you have velocity through the string

hope that helps
 

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