17.10 - Summary
The principle of linear superposition says that whenever waves travel through a
medium, the net displacement of the medium at any point in space and at any time
is the sum of the individual wave displacements. The superposition of waves
explains the phenomenon of interference.
Destructive interference occurs when two waves in the same medium cancel each
other, either partially or fully. If two sinusoidal waves have the same wavelength,
destructive interference will happen when the waves are close to being completely
out of phase, meaning that their phase constants differ by ʌ radians (or 180°).
Constructive interference occurs when two waves in the same medium reinforce
each other. This happens when the waves are close to being in phase for waves
with the same wavelength.
Intermediate interference is a general term for a situation where the difference
between the phases of two interfering waves, called the phase shift, is somewhere
between 0 and ʌ radians.
When two identical waves traveling in opposite directions in the same medium
interfere, they produce a standing wave. In standing waves, there are points called
nodes that experience no displacement at all. The points that experience the
maximum displacement are called antinodes. Standing waves can be either
transverse, as with the oscillations of a piano string, or longitudinal, as with the
sound waves in an organ pipe.
Identical waves from different sources can interfere with each other at a point in space based on the distances they travel to that point, called
their path lengths. Provided they start out in phase, if the path lengths of two waves to a certain point differ by an integer number of
wavelengths, they will constructively interfere at that point. If the path lengths differ by a half-integer number of wavelengths, they will exhibit
completely destructive interference.
Another type of interference occurs when two waves have different frequencies. In this case, beats are produced. The waves alternate
between constructive and destructive interference.HarmonicsInterferenceConstructive:ǻp = nȜ
Destructive:
Beat frequencyfbeat = f 1 – f 2
(^332) Copyright 2000-2007 Kinetic Books Co. Chapter 17