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double the distance

double the distance. reduce intensity by a factor of 4. BUT Half of intensity does not “feel” like half as loud !. Before going into other properties like interference, diffraction, … we will make a mathematical excursion (basically covered in Chapter 1 of Berg&Stork). How to read graphs.

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double the distance

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

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

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

  4. visual analytical

  5. WATCH !!! same information

  6. 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 ?

  7. Wavetools http://www.physics.mcgill.ca/~grant/225B/Wavetools/Computerstuff.html

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

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

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

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

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

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

  14. “Pure” tones are sine waves Harmonic oscillator

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

  16. phase amplitude frequency

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

  18. Beats

  19. Tartini tones

  20. Back to sound (wave) properties … • reflection • refraction • 1/r2 law • diffraction • interference • Doppler effect

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

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

  23. Doppler effect

  24. Doppler effect applethttp://www.lon-capa.org/~mmp/applist/doppler/d.htm

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

  26. mostly constructive interference mostly destructive interference l l

  27. Diffraction • Larger wavelength (~ obstacles) : more diffraction • Shorter wavelength (<< obstacles) : less diffraction

  28. Ultrasound and sonograms Typical frequencies: 300 MHz

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

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