Standing Waves on a Violin String

[kikko]

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 20^oC room hears a note with a wavelength of 60.0 cm.

Homework Equations

Wavelength_m = (2L/m)
f₁ = (v/2L) = (1/2L)(sqrt(T_s/(m/L)

The Attempt at a Solution

(((2Lf)^2)M)/L


What am I doing something wrong?

 

[hy23]

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...

 

[kikko]

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.

 

[hy23]

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