A guitar string has a mass per length of 2.33 × 10−3 kg/m and a fundamental frequency of 146.8 Hz when it is under a tension of 82.4 N. The string breaks, and its owner has only a spare string of mass per length 6.79 × 10−3 kg/m.
(a) In order to use the new string to play the same note, should the string tension be greater than, less than, or equal to 82.4 N? Explain.
(b) What tension should the 6.79 × 10−3 kg/m string have so that its fundamental frequency is 146.8 Hz?