In science Bob learns that the energy of a wave is directly proportional to the square of the waves amplitude. If the energy of a wave is 4 J what should he predict as the amplitude of the wave?

If the energy of the wave is 4 J and the energy is directly proportional to the square of the wave's amplitude, the square root of the energy divided by the proportionality constant should give the amplitude. In this case, if the proportionality constant is 1, the amplitude would be 2 units.