Beginners Guitar Lessons

An unfingered guitar string is 0.70 m long and is tuned to play E above middle C (330 Hz). How far from the end of this string must the finger be placed to play G# above middle C (415 Hz)?

I’m stuck on this one can someone help me out?

Thanks.

For a string fixed at both ends the fundamental frequency is f1 = v/2L

So v/2 = L1*f1 Since the wave speed is constant
we obtain for the second frequency
v/2 = L2*f2

Putting these together L1*f1 = L2*f2 or L2 = L1*f1/f2 = 0.70m*330/415 = 0.56 m

So you must finger the string at 0.70-0.56 = 0.14m from the end

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