2. double the distance reduce intensity by a factor of 4 BUT Half of intensity does not “feel” like half as loud !

3. Before going into other properties like interference, diffraction, … we will make a mathematical excursion (basically covered in Chapter 1 of Berg&Stork)

4. How to read graphs figure what’s in the horizontal axis (w/ units) figure what’s in the vertical axis (w/ units) figure what’s in the vertical axis (w/ units) find the value of “savings” at any particular time find the value of “savings” at any particular time

5. visualanalytical

6. WATCH !!! same information

7. Let us watch now the graph of sound pressure variation as a function of time for some real sounds Which sounds are periodic ? What distinguishes noise from “musical” sounds ? What makes a sound louder ? What makes a sound lower or higher in pitch ?

8. Wavetools http://www.physics.mcgill.ca/~grant/225B/Wavetoo ls/Computerstuff.html

9. A very “pure” (but annoying) sound:

10. “Musical” sounds (“tones”) are periodic period (T) amplitude (A) frequency (f) = 1/T, T=1/f

11. The mathematics of periodic waves wavelength: distance between two crests period: time between two crests frequency: how many crests per second

12. Period (T) = time for one cycle (measured in s, …) Frequency (f) = number of cycles per second (measured in 1/s = Hz) Example

13. amplitude = loudness frequency = pitch shape = timbre With a few qualifications …

14. It is a good time now to read Berg & Stork, Chapter 1

15. “Pure” tones are sine waves Harmonic oscillator

16. [Using a wave generator, find the lowest and highest audible frequencies and calculate their period and wavelength]

17. amplitudefrequency phase

19. How sounds combine: adding two waves 300 Hz 450 Hz 300 Hz + 450 Hz

20. Beats

21. Tartini tones

22. Back to sound (wave) properties … reflection refraction 1/r 2 law diffraction interference Doppler effect

23. Waves interfere: constructively (amplitudes have the same sign and enhance the wave) destructively (amplitudes have opposite sign and partially or completely cancel)

24. Interference movie http://www.colorado.edu/physics/2000/schroedinger/ big_interference.html Interference applet http://www.falstad.com/ripple/ex-2source.html

25. Doppler effect

26. Doppler effect applet http://www.lon- capa.org/~mmp/applist/doppler/d.htm

27. [go to the blackboard and do some real physics] Applications: Doppler radar Doppler radar Doppler sonogram Doppler sonogram Expansion of the Universe Expansion of the Universe

28. mostly constructive interference mostly destructive interference

29. Larger wavelength (~ obstacles) : more diffractionLarger wavelength (~ obstacles) : more diffraction Shorter wavelength (<< obstacles) : less diffractionShorter wavelength (<< obstacles) : less diffraction Diffraction

31. Ultrasound and sonograms Typical frequencies: 300 MHz

32. It is a good time now to read Berg & Stork, Chapter 2.4, 2.5, 2.6, 2.7, 2.8, 2.9