Skip to main content

Learning Introductory Physics with Activities

Paul J. Emigh, Rebecka Tumblin, Kathryn Hadley, Danielle Skinner

Section 7.8 Path Length Difference

The phase difference between two waves that gives rise to interference can be due to two sources:
  1. The initial (natural) phase difference, arising from the where in its cycle each wave begins
  2. The path length difference, \(\Delta D\text{:}\) the difference in distances traveled by the two waves from their source to the point of interference.
The phase difference due to a path length difference can be calculated as
\begin{equation*} \Delta \phi = 2\pi\frac{\Delta D}{\lambda} \end{equation*}
Often, the initial (natural) phase difference is 0, in which case interference will be entirely due to the path length difference.

Exercises Activities

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.
Answer.
Complete destructive interference!
<Prev^TopNext>