A violinist places her finger so that the vibrating section of a 1.1g/m string h

Question

A violinist places her finger so that the vibrating section of a 1.1g/m string has a length of 30cm, then she draws her bow across it. A listener nearby in a 20 degree celcius room hears a note with a wavelength of 50cm.What is the tension in the string?

I think what is getting me here is conversion facors. I'm not sure which all have to be converted, if any. I know cm need to be in m, but I don't know if g/m needs to be in kg/m for mass-density. I think you can solve the wavelength by using the velocity of sound and the frequency, and then, using that, solve tension using V=(sqrt) tention/massdensity, but I can't seem to get it to work. Thanks for any help you can offer.

Explanation / Answer

The equation for the fundamental frequency of an ideal taut string is:

f = (TL/m)/2L


also, f = v/     v=speed of sound in air at 20degrees C

so, v/ = (TL/m)/2L

so, (2Lv/)^2 = TL/m

so, T = (2Lv/)^2*m/L = (2*.3*343.2/.5)^2*1.1*10^-3= 186.6N

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