Chapter 17 Superposition & Standing Waves
Superposition & Standing Waves Superposition of Waves Standing Waves MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 2
Wave Interference MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 3
Constructive Interference MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 4
Destructive Interference MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 5
Acoustic (Sound) Wave Interference MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 6
Sound Wave Sound waves can be considered from a pressure variation or an air displacement point of view. MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 7
Constructive Interference Common source to maintain phase relationship in both speakers. MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 8
Destructive Interference MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 9
Detailed Interference Geometry Constructive Destructive MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 10
Interference in a Ripple Tank MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 11
Interference & Diffraction http://www.pas.rochester.edu/~ksmcf/p100/java/optics/diffraction.html MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 12
http://www.austincc.edu/mmcgraw/simulations/wave-interference.jar MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 13
Beats MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 14
Beats MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 15
Beat Frequency Example By placing a small piece of putty on one of the tuning forks the increased mass causes its frequency to decrease slightly. MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 16
Beat Frequency Two waves of different frequency Superposition of the above waves The beat frequency is f = f 1 f2 MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 17
MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 18
Standing Wave on a String MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 19
Tunable Standing Wave Generator MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 20
MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 21
MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 22
Fourier Analysis MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 23
Fourier Analysis Every waveform can be broken down into its frequency components. MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 24
Fourier Analysis - Square Wave MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 25
Frequency Component Amplitude MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 26
Wave Components in Frequency Space Fourier Analysis MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 27
Musical Instruments MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 28
Pressure Variations in a Pipe MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 29
Open Pipe Resonator MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 30
Closed Pipe Resonator MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 31
Open and Closed Pipes Resonance States fundamental frequency f o 1st harmonic fundamental frequency f o 1st harmonic 2nd harmonic f 1 = 2f o 3rd harmonic f 1 = 3f o 3th harmonic f 2 = 3f o 5th harmonic f 2 = 5f o MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 32
Pipe Resonator Calculations Natural frequency dependent on length of pipe For closed pipe - no "even harmonics Fundamental frequency is a half-loop or ¼ L. Since every harmonic represents the addition of a complete loop, which contains two half-loops, we can never add just one more half-loop. Thus, we cannot generate even harmonics in closed pipes. MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 33
Pipe Resonator Calculations MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 34
Open Pipe Resonator MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 35
Closed Pipe Resonator MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 36
Musical Instruments Frequency Components MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 37
Fundamental Wave and the 4th Harmonic MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 38
Musical Instrument Waveforms Violin Trumpet Clarinet MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 39
Frequency Component Structure Violin Clarinet Organ Pipes Piano MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 40
Typical Musical Overtone Structures MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 41
Musical Sound Waveforms MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 42
Musical Sound Frequency Spectrum MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 43
Fourier Analysis http://www.austincc.edu/mmcgraw/simulations/fourier.jar MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 44
Standing Wave Patterns MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 45
Ringing Bell - Resonant Modes MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 46
Guitar - Resonant Modes MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 47
MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 48