Fundamental Frequency and Sound

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DeathandTaxes

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I don't understand where the relationship between f and r is obtained? Does it mean f and p (density)? If so, then I would see why we need to increase the density... but why is it the density of the strings and not the wood?
 
In this case, the equation gives you that all of the quantities affecting frequency are only dependent on the material properties of the string. Thus, you would assume that to change the frequency, you would only change the material property of the strings. Furthermore, remember for all sound waves, that the properties of the wave are dependent upon the material in which it travels--in this case it is the string not the wood itself.
 
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