When two waves interfere, the resulting amplitude of the wave at any given point depends on the superposition of the individual wave amplitudes at that point. The interference can be constructive or destructive, resulting in different amplitudes.
- Constructive Interference: Constructive interference occurs when two waves with the same frequency and in-phase (their crests and troughs align) combine to create a wave with an increased amplitude. Mathematically, when two wave amplitudes add up, the resulting amplitude (A) is calculated as the sum of the individual wave amplitudes (A₁ and A₂) at that point:
A = A₁ + A₂
The resulting amplitude is greater than either individual wave's amplitude.
- Destructive Interference: Destructive interference occurs when two waves with the same frequency and out-of-phase (their crests and troughs are misaligned) combine to create a wave with a decreased amplitude or even complete cancellation. Mathematically, when two wave amplitudes subtract from each other, the resulting amplitude (A) is calculated as the difference between the individual wave amplitudes (A₁ and A₂) at that point:
A = A₁ - A₂
The resulting amplitude can be smaller than the amplitude of the individual waves, and in the case of complete cancellation, the resulting amplitude can be zero.
It's important to note that these calculations assume the waves are traveling through the same medium and have the same frequency. Additionally, the actual amplitude at any given point may depend on the specific phase relationship and the spatial distribution of the interfering waves.