Interference of waves.

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Presentation transcript:

Interference of waves

Interference of waves Standing electron waves on a copper surface with iron atoms added, viewed by scanning tunneling microscope.

Principle of superposition (addition) Path-length dependence Constructive Destructive

Measurements of movement, distortions

Holograms

Two speakers are on a line (not stereo) Two speakers are on a line (not stereo). Both emit the same sound waves (v=300 m/s) at 500 Hz. P1. What is the wavelength?____m A: 0.3 B: 0.6 C: 1.2 D: 3.0 E: 6.0 P2. How far back should one speaker be moved to get a minimum in sound for this direction ? _____ m A: 0.3 B: 0.6 C: 1.2 D: 3.0 E: 6.0

What will the does the boy hear if he and the speakers stay put, but f changes?

Standing waves on a rope or string Harmonics Resonance condition: “Integer number of ________________ fit into L.” n=1,2,3,... the resonant f’s

Standing waves in air Open-open pipes Resonance condition: “Integer number of ________________ fit into L.” n=1,2,3,... the resonant f’s

Standing waves in air Closed-open pipes Resonance condition: “Odd integer number of ________________ fit into L.” n=1,3,5,... the resonant f’s

Other examples of resonance Swings Springs Communications signal detection How the “whistle” on a flute or organ pipe works

You change the frequency that you excite a tube, and find three consecutive resonant frequencies at 450, 750, and 1050 Hz. P3. What is the fundamental frequency? _____ Hz (Hint: these are all integer multiples of the same fundamental) A: 50 B: 75 C: 150 D: 300 P4. Is this an open-open pipe, or a closed-open pipe? (Hint: how does the spacing compare to the fundamental) a. open-open pipe b. closed-open pipe

1 m

From two sounds with slightly different f’s. Beats From two sounds with slightly different f’s. Applications of beats: Tuning Measuring Doppler shifts in radar, ultrasound

Why do voices and instruments sound different for the same pitch?

“Strange-sounding” instruments: bells, gongs, blocks Normal instrument Non-harmonic instrument (bell) These harmonics are not multiples of fundamental! Maple Leaf Rag on a bell's "scale"