Often, the initial (natural) phase difference is 0, in which case interference will be entirely due to the path length difference.
Principle7.8.1.Maximum Constructive Interference.
If the initial phase difference between two waves is zero, maximum constructive interference occurs at locations in space where the path length difference is an integer multiple of the wavelength
If the initial phase difference between two waves is zero, complete destructive interference occurs at locations in space where the path length difference is a half-integer multiple of the wavelength
\begin{equation*}
\Delta D = \pm \lambda/2, \pm 3\lambda/2, ...
\end{equation*}
ExercisesActivities
1.
You are standing halfway between two sources of waves with the same frequency and amplitude. You observe destructive interference at your location. Explain how this is possible.
2.
Two waves with the same initial phase, frequency, and amplitude reach you by traveling different distances. One wave traveled \(4 \mathrm{~m}\) to reach you and the other wave traveled \(5.5 \mathrm{~m}\) to reach you. The wavelength is \(0.5 \mathrm{~m}\text{.}\) What kind of interference do you see? Explain your reasoning.
Answer.
Maximum constructive interference!
3.
The wavelengths of the waves in the previous activity are changed to \(1 \mathrm{~m}\text{.}\) What kind of interference do you see now? Explain your reasoning.
