Standing Waves Review Harmonic Oscillator Review Traveling Waves

Standing Waves • • Review Harmonic Oscillator Review Traveling Waves Formation of Standing Waves and Resonance Variables String instruments Examples Standing Waves and Electron Orbitals

Summary - Simple Harmonic Oscillator •

Summary – Traveling Waves •

Traveling wave animation http: //www. animations. physics. unsw. edu. au/waves-sound/travelling-waves. II

Travelling Standing Waves http: //phet. colorado. edu/sims/wave-on-a-string_en. html • Travelling wave – No end – Zero damping – Oscillate • Standing wave – Clamped end – Some damping – Oscillate

Formation of Standing Wave •

Standing wave animation • Animation http: //faraday. physics. utoronto. ca/IYear. Lab/Intros/Standing. Waves/Flash/reflect. html • Note Peaks oscillate in place – Nodes – Antinodes • Only certain wavelengths “fit” – Basis for stringed instruments (guitar/violin/piano) – Electromagnetic resonances – Quantum mechanics

Standing wave with both fixed ends • Both ends (approximately) fixed http: //faraday. physics. utoronto. ca/IYear. Lab/Intros/Standing. Waves/Flash/sta 2 fix. html • Only certain wavelengths “fit”

Standing waves and resonance •

Standing waves and resonance •

Stringed Instruments •

Stringed Instruments II • Factors effecting frequency – String length (guitar frets) – Tension (violin tuning) – Mass/length (bass guitar)

Example 11 -14 •

Problem 53 •

Problem 56 •

Problem 58 •

Problem 59 • Find velocity needed for number of antinodes • Find tension needed for those velocities

Problem 59 (2) •

Problem 59 (3) •

Standing waves and electron orbitals http: //www. upscale. utoronto. ca/PVB/Harrison/Flash/Quantum. Mechanics/Circular. Stand. Waves/ Circular. Stand. Waves. html (sorry the downloadable. swf doesn’t seem to work)