Determine Tension and Length of 50g Guitar String Oscillates at 1280Hz

[Ry122]

a third harmonic of a 50g guitar string oscillates at a frequency of 1280hz. the wavelength is 30cm
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?

 

[davieddy]

I can't spot an error, the original question sounds plausible
and yet this tension is ridiculously high.
50g sounds a bit heavy, but even so...

 

[nlightner]

Your calculations are correct, but the value for tension does seem quite large. It is possible that there may be some error in the given values, such as the frequency or wavelength being slightly off. It may also be helpful to double check your unit conversions to ensure they are correct. If all the values and calculations are correct, then it is possible that the tension in the string is simply very high, which is not uncommon for guitar strings. It would be helpful to compare this value to the typical tension range for guitar strings to see if it falls within a reasonable range.