The elastic limit of the aluminum forming a piece of wire is equal to 2.5 108 Pa. What is the maximum speed at which transverse wave pulses can propagate along this wire without exceeding this stress

At 20∘c, the hole in an aluminum ring is 2.800 cm in diameter. you need to slip this ring over a steel shaft that has a room-temperature diameter of 2.804 cm . 1. to what common temperature should the ring and the shaft be heated so that the ring will just fit onto the shaft? coefficients of linear thermal expansion of steel and aluminum are 12×10−6 k−1 and23×10−6 k−1 respectively.