Chapter 17. Superposition & Standing Waves
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1 Chapter 17 Superposition & Standing Waves
2 Superposition & Standing Waves Superposition of Waves Standing Waves MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 2
3 Wave Interference MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 3
4 Constructive Interference MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 4
5 Destructive Interference MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 5
6 Acoustic (Sound) Wave Interference MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 6
7 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
8 Constructive Interference Common source to maintain phase relationship in both speakers. MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 8
9 Destructive Interference MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/2012 9
10 Detailed Interference Geometry Constructive Destructive MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
11 Interference in a Ripple Tank MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
12 Interference & Diffraction MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
13 MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
14 Beats MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
15 Beats MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
16 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/
17 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/
18 MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
19 Standing Wave on a String MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
20 Tunable Standing Wave Generator MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
21 MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
22 MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
23 Fourier Analysis MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
24 Fourier Analysis Every waveform can be broken down into its frequency components. MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
25 Fourier Analysis - Square Wave MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
26 Frequency Component Amplitude MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
27 Wave Components in Frequency Space Fourier Analysis MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
28 Musical Instruments MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
29 Pressure Variations in a Pipe MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
30 Open Pipe Resonator MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
31 Closed Pipe Resonator MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
32 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/
33 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/
34 Pipe Resonator Calculations MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
35 Open Pipe Resonator MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
36 Closed Pipe Resonator MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
37 Musical Instruments Frequency Components MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
38 Fundamental Wave and the 4th Harmonic MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
39 Musical Instrument Waveforms Violin Trumpet Clarinet MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
40 Frequency Component Structure Violin Clarinet Organ Pipes Piano MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
41 Typical Musical Overtone Structures MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
42 Musical Sound Waveforms MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
43 Musical Sound Frequency Spectrum MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
44 Fourier Analysis MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
45 Standing Wave Patterns MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
46 Ringing Bell - Resonant Modes MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
47 Guitar - Resonant Modes MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
48 MFMcGraw-PHY 2425 Chap 17Ha - Superposition - Revised: 10/13/
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