When two waves are out of phase with each other, their amplitudes add up because the positive peaks of one wave align with the negative peaks of the other wave. This results in constructive interference, where the amplitudes reinforce each other, leading to a larger combined amplitude.
On the other hand, when two waves are in phase with each other, their amplitudes subtract or cancel out. This occurs because the positive peaks of one wave align with the positive peaks of the other wave, and the negative peaks align with the negative peaks. This leads to destructive interference, where the amplitudes interfere with each other and result in a smaller or zero combined amplitude.
To understand this concept better, let's consider the following scenarios:
Out of Phase: Suppose two waves of equal amplitude and frequency are out of phase by 180 degrees (opposite phase). When the positive peak of one wave coincides with the negative peak of the other wave, they add up, resulting in a larger combined amplitude. Conversely, when the positive peak of one wave aligns with the positive peak of the other wave, and the negative peak aligns with the negative peak, they subtract or cancel out, resulting in a smaller or zero combined amplitude.
In Phase: If the same two waves are in phase (aligned in phase), their positive peaks align with each other, as do their negative peaks. As a result, they interfere constructively, adding up to a larger combined amplitude.
The interaction between waves in terms of addition or subtraction of amplitudes depends on the phase relationship between the waves. Out-of-phase waves tend to add up, while in-phase waves tend to subtract or cancel out. This behavior is a fundamental principle of wave interference and can be observed in various physical phenomena, such as interference patterns in light or sound waves.