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Guitar string: Harmonic frequency, tension force, length of string

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SEE ATTACHMENT #1 for the general form of the equation of standing waves.

A standing wave is set up in a guitar string. Find the first harmonic frequency. Then for a new frequency find new string tension and length.

A guitar string is .64 m long and has a linear density of .0004 kg/m. The tension is set at 55 newtons.

PART a. Find the frequency of the first harmonic, the fundamental note emitted.
PART b. Find the tension force required for the string to emit a fundamental note, or first harmonic, of 350 cy/sec.
PART c. With tension at 55 nt, you press a fret to shorten the length for which the fundamental is 350 cy/sec. Find the new length.

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Each part of the problem is solved with explanation and computations to arrive at the answers.

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Using (2) from ATTACHMENT #2, you should substitute ...

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