A piano string is steel wire with radius 0.50 mm and length 1.2 m. It is under

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A piano “string” is steel wire with radius 0.50 mm and length 1.2 m. It is under 800 N of tension. 

(a) What is the speed of transverse waves on the string?

(b) What is the fundamental frequency for transverse waves?

(c) What is the speed of longitudinal waves (i.e., sound) in the wire? Consider the wire to be a thin solid steel rod. 

(d) Assuming nodes at the ends, what is the fundamental frequency for longitudinal waves? (Longitudinal waves in the wire do contribute to the characteristic sound of the piano.)

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