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Two wires are anchored at both ends. Wire 1 has a mass of 85 grams and a length of 5.2 meters. Wire 2 has a mass of 50 grams, a length of 20 meters and a tension of 155 N. What must be the tension (to the nearest newton) in Wire 1 if its third harmonic is to equal the first overtone of Wire 2?

Added Sun, 05 Jul '15

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For wire 2...

v = sqrt(T/u)

v = sqrt[(155)/(.05/20)]

v = 249 m/s

v = f(wavelength)

The Wavelength of the first overtone is the string length = (20 m)

249 = f(20)

f = 12.45 Hz

The third harmonic is the second overtone. The second overtone has a wavelength of 2/3 of the string length

(2/3)(5.2) = 3.47 m

v = f(wavelength)

v = (12.45)(3.47) = 43.16 m/s

v = sqrt (T/u)

43.16 = sqrt(T/.085/5.2)

Added Sun, 05 Jul '15

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