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?

The energy of a wave is directly proportional to the square of the waves amplitude. Therefore, E = A² where A is the amplitude. This therefore means when the amplitude of a wave is doubled the energy will be quadrupled, when the amplitude is tripled the energy increases by a nine fold and so on.
Thus, in this case if the energy is 4J, then the amplitude will be  √4 = 2 .