Why Does My Calculation of Wire Length Differ from the Textbook's Answer?

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SUMMARY

The calculation of wire length based on tension and frequency was analyzed, revealing a discrepancy between the calculated length of 0.36 m and the textbook's answer of 0.65 m. The correct formula for wire length in terms of overtone frequency is L = n*v/(2*fn), where n represents the harmonic number. The discussion clarified that the third overtone corresponds to the fourth harmonic, which was a critical point in the calculation. The final formula presented in the attempt was noted to be incorrectly written, but the solution for n=3 was confirmed as correct.

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[SOLVED] length of wire

Homework Statement



A wire of mass 1.1 g is under a tension of 100 N. If its third overtone is at a frequency of 750 Hz, calculate the length of the wire.

The Attempt at a Solution



v = sqrt(FL/m) = 301.5*sqrt(L)

fn = n*v/(2*L) --> L = n*v/(2*fn) --> L = 0.36 m

The book says 0.65 m. Am I wrong?
 
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The third "overtone" is the fourth "harmonic."

Other than that, you did everything right. (well, your final formula is incorrectly written, but you solved correctly for n=3.)
 
Last edited:

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