NOTES 28, Wave Interactions
Objective 1: Know the terminology used to describe wave interactions.
a) Constructive interference – Interference in which individual displacements on the same side
of equilibrium are added together to form the resultant wave.
b) Destructive interference – Interference in which individual displacements on opposite sides of
equilibrium are added together to form the resultant wave.
c) Standing wave – A wave pattern that results when two waves of the same frequency,
wavelength, and amplitude travel in opposite directions and interfere.
d) Node – A point in a standing wave that always undergoes complete destructive interference
and therefore is stationary.
e) Anti-node – A point in a standing wave, halfway between two nodes at which the largest
amplitude occurs.
f) Phase angle – Used to describe how two waves interfere. If two waves are exactly in phase,
their interference will be completely constructive. If they are 180 exactly out of phase, their
interference will be completely destructive.
g) Coherent sources – Sources that produce waves either exactly in phase or exactly out of
phase.
Objective 2: Apply the principle of superposition for waves that interfere in a medium.
a) When two or more waves are present simultaneously at the same place, the resultant
disturbance is the sum of the disturbances from the individual waves.
b) Displacements in the same direction produce constructive interference.
c) Displacements in opposite directions produce destructive interference.
Superposition of waves
Noise-canceling headphones utilize destructive interference
Objective 3: Describe the reflection and transmission one one-dimensional waves at a boundary
between two media.
a)
b)
c)
d)
Wave pulses which strike a barrier rebound into the original medium.
At a free boundary, waves are reflected on the same side as the original pulse.
At a fixed boundary, waves are reflected and inverted.
This applies to wave pulses in all media.
Reflection - fixed end
http://www2.biglobe.ne.jp/~norimari/science/JavaEd/e-wave5.html
Transmission/Reflection
http://www.hazelwood.k12.mo.us/~grichert/sciweb/waves.htm
Objective 4: Predict whether specific traveling waves will produce a standing wave.
Objective 5: Describe and identify nodes and antinodes of a standing wave.
a) A standing wave is formed by the superposition (constructive and destructive) of identical
waves traveling in opposite directions. These waves can be the result of the reflection of the
wave train from a fixed or non-fixed barrier.
b) Standing waves have nodes (places of no medium movement) and anti-nodes (places of
double amplitude).
c) Standing waves do not appear to move along or through the medium compared to the traveling
waves that produce them.
d) Only certain frequencies produce standing wave patterns. The wavelength of these standing
waves depends on the string length.
1. 1st harmonic (fundamental) – wavelength is 2L
2. 2nd harmonic – wavelength is L
3. 3rd harmonic – wavelength is ⅔ L