A steel wire in a piano has a length of 0.6000 m and a mass of 3.200 ? 10-3 kg. To what tension must this wire be stretched in order that the fundamental vibration correspond to middle C (fC = 261.6 Hz on the chromatic musical scale)?

University Physics Volume 1
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Chapter16: Waves
Section: Chapter Questions
Problem 144CP: A copper wire has a radius of 200 µ m and a length of 5.0 m. The wire is placed under a tension of...
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A steel wire in a piano has a length of 0.6000 m and a mass of 3.200 ? 10-3 kg. To what tension must this wire be stretched in order that the fundamental vibration correspond to middle C (fC = 261.6 Hz on the chromatic musical scale)?

Expert Solution
Step 1 - Given quantities

Given :

Length ( L ) = 0.6 m

Mass ( m ) = 3.2 * 10-3 kg

Frequency ( fC ) = 261.6 Hz 

From the formula of Frequency :

f = 12L * (Tμ)  ;  where T = Tension forcef = 12L * (TmL)

 

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