Tension In musical strings and wavelength

[jrjay09]

Homework Statement

One string of a certain musical instrument is 79.0cm long and has a mass of 8.79g . It is being played in a room where the speed of sound is 344m/s .
A)To what tension must you adjust the string so that, when vibrating in its second overtone, it produces sound of wavelength 3.39cm ?
B)What frequency sound does this string produce in its fundamental mode of vibration?

Homework Equations

v=sqroot(Tension/linear density), linear Density=m/L, v=(f)(lamda)=(omega)/k, k=2(pi)/(lamda)

The Attempt at a Solution

I keep trying to get out a way to find T but always end up reducing an eqaution to something pointless such as f=f or (lamda)=(lamda). My real problem is a concept one...Is the v used in equations the speed of sound in the room (334m/s) and when finding linear density do I use .79m or .0339m as the length. Please respond..anything helps and thank you.

 

[Delphi51]

The v must be the velocity of the wave on the string when referring to the wave on the string. But use 344 m/s for the sound "of wavelength 3.39 cm". Use 8.79g/79 cm (in standard units) for the linear density of the string.

 

[jrjay09]

I tried using 344m/s as the v in the eqaution v=sqroot(Tension/linear denstiy)

so... v^2 = Tension/Linear Density
so... Tension= v^2 (linear Density) => tension= (344m/s^2)(.00879kg/.79m)=1316.67N.
However when I tried that it was wrong. I am still confused about the "of wavelength 3.39cm" and the second overtone. Don't they need to come into the problem too? Thank you

 

[Delphi51]

I tried using 344m/s as the v in the eqaution v=sqroot(Tension/linear denstiy)

You are mixing the sound and the vibration on the string incorrectly.
The thing they have in common is the frequency. Use v = f*lambda for the sound with v=344 and lambda = .0339 to get the frequency for both the wave AND the vibration. Then use that frequency with formulas that apply to the vibrating string.