STANDING WAVES AND CHLADNI FIGURES

Nick Irwin PHYS101 Learning Object LO6

• 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 wavesSEE: http://academic.greensboroday.org/~regesterj/potl/Waves/DiffractionInterference/standing_wave.gif

PART I: STANDING WAVES

• 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

PART II: CHLADNI PLATES - BACKGROUND• 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

PART II: CHLADNI PLATES - EXPLANATION• 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

PART II: CHLADNI PLATES - EXPLANATION• 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)

PART II: CHLADNI PLATES - APPLICATION• 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