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 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

visualanalytical

WATCH !!! same information

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 ?

Wavetools ls/Computerstuff.html

A very “pure” (but annoying) sound:

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

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

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

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

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

“Pure” tones are sine waves Harmonic oscillator

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

amplitudefrequency phase

How sounds combine: adding two waves 300 Hz 450 Hz 300 Hz Hz

Beats

Tartini tones

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

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

Interference movie big_interference.html Interference applet

Doppler effect

Doppler effect applet capa.org/~mmp/applist/doppler/d.htm

[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

mostly constructive interference mostly destructive interference

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

Ultrasound and sonograms Typical frequencies: 300 MHz

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