Standing waves

Some phase issues 

Normal modes 

Resonance of open-close tube and Amplitude size 

Generation of standing waves with two travelling waves 

Generation of standing wave by reflection of a travelling wave   

Simulation node-node and node-anti node    

Waves on a string-phet 

Harmonics - modes - overtones 

Notations for modes and harmonics 

Copilot: Normal modes 1           Normal modes 2 

Modes  Harmonics

Modes and harmonics 2

Formal definition of Mode and Harmonics

Modes - harmonic vs non harmonic

Normal modes and integers

Frequency degeneracy

Modes of complex systems

Mode is equivalent of spatial profile of the wave.

Harmonics is more about the frequency

Internal vs boundary Nodes

No direction of motion

No energy transfer

Position dependent amplitude and envelope 

All particles have the same frequency. Only in phase or out of phase.

Nodes have zero amplitude          

Anti-nodes have maximum amplitude           

Distance between two nodes          Distance between node and antinode         

Standing waves on a string or rope           

Harmonics are only  node-node. Fundamental frequency       f1= v / 2L              fn = n * f1           

Standing waves in a air column        Harmonics can be node-antinode    Fundamental frequency       f1= v / 4L              fn = (2n -1 ) * f1         

Harmonics can also be node-node or antinode-antinode