When two waves with equal amplitude but opposite directions are added together, they undergo a process called destructive interference. Destructive interference occurs when the crests of one wave align with the troughs of the other wave, causing them to cancel each other out. As a result, the amplitudes of the two waves subtract from each other, resulting in a net amplitude of zero at specific points in space.
Mathematically, if we denote the amplitude of the waves as A, and one wave has a positive amplitude (+A) while the other has a negative amplitude (-A), the resulting wave can be represented as:
Resulting wave = (+A) + (-A) = 0
Therefore, the result of adding two waves with equal amplitude but opposite directions is a wave with zero net amplitude.