Guitar Strings Tubes
September 14th, 2010
How much tension should be in the string if it is to produce resonance?
A 76.9 cm long guitar string of mass 2.23g is placed near a tube open at one end, and also 76.9 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?
The wavelength of the note produced in the string = 2*.769 m
The velocity of the waves in the string = sqrt ( T / ( 0.00223 / 0.769 ) )
Frequency = sqrt ( T / ( 0.00223 / 0.769 ) ) / (2*0.769)
Frequency of the wave of the tube = 330 / (4*0.769 / 5)
So
330 / (4*0.769 / 5) = sqrt ( T / ( 0.00223 / 0.769 ) ) / (2*0.769)
Solving, T = 1973.724 N
Big Strings` Tubes©
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