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?
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