A high-carbon steel wire of length 1.20 m and circular cross-section is to be used in a musical instrument. The desired speed of transverse waves on the wire is 120 m/s. The wire has a diameter of 0.80 mm, and the density of high-carbon steel is 7.8 × 10³ kg/m³.
(a) Determine the mass per unit length of the wire.
(b) Calculate the tension that must be applied to achieve the desired wave speed.
(c) In the laboratory setup, the tension will be produced by hanging a mass over a light, frictionless pulley. Determine the mass that must be suspended to provide the required tension, and comment on whether the mass is reasonable for typical instrument construction.