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

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The calculation of wire length based on the given parameters resulted in a length of 0.36 m, while the textbook states it should be 0.65 m. The user correctly applied the formula for wave speed and frequency but misinterpreted the overtone terminology, confusing the third overtone with the fourth harmonic. The final formula presented was also noted to be incorrectly written. Clarification on the harmonic series and proper formula usage is essential for accurate results.
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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.)
 
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