1. Interference of waves

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

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

4. Measurements of movement, distortions

5. Holograms

6. 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

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

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

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

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

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

13. 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

14. 1 m

15. 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

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

17. “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"