Yes, the amplitude of the resultant wave can be greater than either of the amplitudes of the original waves when two waves interfere. This phenomenon is known as constructive interference.
Constructive interference occurs when the crests of one wave align with the crests of another wave, or the troughs align with the troughs. In this case, the amplitudes of the two waves add up, resulting in a larger combined amplitude in the resultant wave.
Mathematically, if we consider two waves with amplitudes A1 and A2, and they interfere constructively, the amplitude of the resultant wave, A_res, can be calculated using the formula:
A_res = A1 + A2
In constructive interference, the amplitudes of the waves add up, resulting in an increased amplitude in the resultant wave. The actual amplitude of the resultant wave depends on the specific characteristics and relative amplitudes of the interfering waves.
It's important to note that this is true for waves that have the same frequency or very close frequencies, and their peaks and troughs align precisely or almost precisely. If the waves are out of phase or have a phase difference, the amplitude of the resultant wave can be smaller than the individual waves, which is known as destructive interference.