Solve Standing Wave Problem: Fundamental Frequency & Tension of String

physstu
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Hi, I have been staring at this problem for 2 hours now, and I feel like it is really simple, but I cannot quite wrap my head around it...here it is

A violinist places her finger so that the vibrating section of her 1.0 g/m string has a length of 30 cm, then she draws her bow across it. A listener nearby in a 20 degrees C room hears a note with a wavelength of 40 cm. What is the tension in the string?


I have been messing around with a couple different equations. The one I am pretty sure I need to use is:

Fund. Freq. = v/2L = 1/2L * \sqrt{T_{s}/linear density}

So I figured if I could somehow get v (speed of the wave on the string) or the fundamental frequency, I could solve for the tension of the string. This is where the problem is I have no idea how to do that, because as far as i know the speed of a wave on a string depends on the Tension of the string, which brings us back to what we need in the first place...

Any advice at all would be appreciated because I am really stumped.
Thanks!
 
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I think you have to make an assumption about the speed of sound in air, base don the given temperature...

This will give you the frequency, form which you should be able to get tension
 

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