Chapter 15, Problem 15.72P

Holding Up Under Stress. A string or rope will break apart if it is placed under too much tensile stress [see Eq. (11.8)]. Thicker ropes can withstand more tension without breaking because the thicker the rope, the greater the cross-sectional area and the smaller the stress. One type of steel has density 7800 kg/m³ and will break if the tensile stress exceeds 7.0 × 10⁸ N/m². You want to make a guitar string from 4.0 g of this type of steel. In use, the guitar siring must be able to withstand a tension of 900 N without breaking. Your job is to determine (a) the maximum length and minimum radius the string can have; (b) the highest possible fundamental frequency of standing waves on this string, if the entire length of the string is free to vibrate.