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determine the tension in the string and the string length.

my attempt:

the 3rd harmonic of a guitar string is 3/2 times the wavelength so the length of the string is 45cm.

so mass per unit length is .05/.45=.111kg/m

v=f(lambda)

so v =384ms^1

V=sqrt(T/mu)

so 384=sqrt(T/.111)

T therefore is =16367.616N

isnt this value for tension too large to be correct?

where am i going wrong?