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)/LWhat 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

 

[rwisz]

I would like to clarify that the equations you have provided are not entirely relevant to the given scenario. The equations you have provided are for calculating the fundamental frequency of a standing wave on a string, but the question does not mention the fundamental frequency or the tension in the string.

To answer the question, we can use the equation for the speed of a wave on a string, v = sqrt(T/µ), where T is the tension in the string and µ is the linear mass density of the string. With the given information, we can calculate the speed of the wave on the string to be v = sqrt(1.00 g/m / 0.40 m) = 2.24 m/s.

Next, we can use the equation for the wavelength of a standing wave on a string, λ = 2L/n, where L is the length of the vibrating section of the string and n is the number of nodes (or anti-nodes) in the standing wave. In this case, the length of the vibrating section is given as 40.0 cm, and we can assume that the fundamental frequency is being produced, which means there is only one node and one anti-node. Therefore, the wavelength of the wave produced is λ = 2(0.40 m) = 0.80 m.

Now, using the equation for the speed of the wave, we can calculate the frequency of the wave as f = v/λ = 2.24 m/s / 0.80 m = 2.8 Hz. This is the frequency of the wave produced by the violin string, which is what the listener would hear as the note.

In conclusion, the listener in a 20oC room would hear a note with a frequency of 2.8 Hz, which corresponds to a wavelength of 60.0 cm. The equations you have provided are not relevant to this scenario, and it is important to use the correct equations and relevant information to solve a problem.