Standing waves form from wave interference when waves reflect off a boundary and interact with incoming waves. They have nodes of smallest amplitude where there is no movement, and antinodes of largest amplitude with greatest movement. Chladni figures are patterns that result from vibrations on a plate and can be explained by standing wave interference. When waves reach the end of the plate they reflect back, interfering to form nodes where sand does not move and antinodes between with movement. Higher harmonics have more complex node patterns.

1. Nick Irwin PHYS101 Learning Object LO6

2. • STANDING WAVE: a wave where each point experiences constant amplitude
• Standing waves form as a result of wave interference  when waves reflect off a
boundary, they go in the opposite direction and will interact with incoming waves
SEE: http://academic.greensboroday.org/~regesterj/potl/Waves/DiffractionInterference/standing_wave.gif
• Standing waves have nodes and antinodes
• NODE: the points with the smallest amplitude (zero)
 the point doesn’t move
• ANTINODE: the points with the largest amplitude
 the point has the greatest movement
= NODE
= ANTINODE

3. • Chladni figures were initially
discovered and subsequently studied
by Robert Hooke and Ernst Chladni
respectively
• Chladni figures are intricate patterns
which result from vibrations on a
plate
• Chladni figures can be explained by
standing waves
• Watch the video on the next slide for
an example
• Later discussion refers to this video
www.thescienceofcreativity.com
www.mat.ucsb.edu

4. • Chladni figures are the result of
standing waves
 waves (of a set frequency) are
propagated through a plate
 as the waves reach the end of
the plate they reflect back
 the reflected waves result in
interference which forms a
standing wave
• Each spot on the plate where the
sand stops moving represents a
node (zero motion)
• The regions without sand indicate
regions of movement (such as the
antinode)
= NODE
= ANTINODE

5. • Using Chladni plates we can visualize different harmonics or resonant frequencies
HARMONICS: the frequency at which the antinode amplitude of the resultant
standing wave is a maximum
2nd HARMONIC
(node = 1)
3rd HARMONIC
(node = 2)
6th HARMONIC
(node = 5)

6. • Chladni figures with greater complexity are caused by the waves reflecting in
different directions
• If mechanical waves are reflected in all three dimensions nodes can be created in
three dimensional space (for example in mid air)
 This means that mid air nodes can be made where the air particles experience
minimal movement
 By placing an object on these mid air nodes, you can cause objects to levitate!
SEE THE NEXT SLIDE FOR A VIDEO