AcademySound
Academy
Interference in Sound
Level 1 - Physics topic page in Sound.
Principle
Sound waves interfere when coherent pressure variations superpose at the same point.
Notation
\(\Delta r\)
path difference
\(\mathrm{m}\)
\(\Delta \phi\)
phase difference
\(\mathrm{rad}\)
\(\lambda\)
wavelength
\(\mathrm{m}\)
\(m\)
integer order
1
\(A\)
pressure-amplitude scale
\(\mathrm{Pa}\)
Method
At a listener, two coherent sound waves add as pressure variations. The phase difference is set by source phase plus path difference.
Path phase
\[\Delta\phi=\frac{2\pi\Delta r}{\lambda}\]
Constructive condition
\[\Delta r=m\lambda\]
Destructive condition
\[\Delta r=\left(m+\frac{1}{2}\right)\lambda\]
Equal amplitudes
\[A_{\mathrm{res}}=2A\left|\cos\left(\frac{\Delta\phi}{2}\right)\right|\]
Stable constructive and destructive regions require the sources to keep a fixed phase relationship.
Rules
These are the compact interference conditions.
Phase difference
\[\Delta\phi=\frac{2\pi\Delta r}{\lambda}\]
Constructive
\[\Delta r=m\lambda\]
Destructive
\[\Delta r=\left(m+\frac{1}{2}\right)\lambda\]
Equal amplitudes
\[A_{\mathrm{res}}=2A\left|\cos\left(\frac{\Delta\phi}{2}\right)\right|\]
Examples
Question
Two in-phase speakers emit
\[680\,\mathrm{Hz}\]
sound in air. At a point, the path difference is \[0.25\,\mathrm{m}\]
Use \[v=340\,\mathrm{m\,s^{-1}}\]
to classify the interference.Answer
The wavelength is
\[\lambda=\frac{v}{f}=\frac{340}{680}=0.50\,\mathrm{m}\]
The path difference is \[0.25\,\mathrm{m}=\lambda/2\]
so the interference is destructive for equal in-phase sources.Checks
- Interference adds pressure variations, not sound levels in decibels.
- Destructive interference needs comparable amplitudes to produce strong cancellation.
- Different frequencies do not produce a fixed spatial cancellation pattern.
- A path difference of one wavelength returns the waves to the same phase.