When two waves interfere with each other, the resulting intensity is determined by the superposition of their individual amplitudes. The relationship between intensity and amplitude depends on whether the interference is constructive or destructive.
Constructive Interference: In constructive interference, the two waves have the same frequency and are in phase with each other. When they overlap, their amplitudes add up, resulting in an increased overall amplitude. The intensity of the resulting wave is directly proportional to the square of the amplitude. Mathematically, the relationship can be expressed as:
I = 4 * I₀ * cos²(θ/2)
where I is the resultant intensity, I₀ is the initial intensity (before interference), and θ is the phase difference between the waves.
Destructive Interference: In destructive interference, the two waves have the same frequency but are out of phase with each other. When they overlap, their amplitudes partially or completely cancel out, resulting in a decreased overall amplitude. The intensity of the resulting wave is directly proportional to the square of the amplitude. Mathematically, the relationship can be expressed as:
I = 4 * I₀ * sin²(θ/2)
where I is the resultant intensity, I₀ is the initial intensity (before interference), and θ is the phase difference between the waves.
In both cases, it's important to note that the relationship between intensity and amplitude assumes that the waves have the same frequency. If the frequencies differ, additional considerations need to be taken into account, such as beat phenomena.