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

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The discussion focuses on calculating the tension and length of a 50g guitar string oscillating at a frequency of 1280Hz, with a wavelength of 30cm. The calculated string length is determined to be 45cm, leading to a mass per unit length of 0.111 kg/m. Using the wave equation, the velocity is found to be 384 m/s, which leads to a tension calculation of approximately 16,367.616 N. Concerns are raised about the tension value being excessively high for a 50g string, prompting a search for potential errors in the calculations. The participants express confusion over the plausibility of the original question given the resulting tension.
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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?
 
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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...
 
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