double the distance reduce intensity by a factor of 4 but half of intensity does not “feel” like...
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double the double the distancedistance
reduce intensity reduce intensity by a factor of 4by a factor of 4
BUT
Half of intensity does not “feel” like half Half of intensity does not “feel” like half as loud !as loud !
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Before going into other properties Before going into other properties like interference, diffraction, … we like interference, diffraction, … we will make a mathematical excursion will make a mathematical excursion (basically covered in Chapter 1 of (basically covered in Chapter 1 of
Berg&Stork)Berg&Stork)
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How to read graphsHow to read graphs
• figure what’s in the horizontal axis (w/ units)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 timefind the value of “savings” at any particular time
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22P x x
visualvisual analyticalanalytical
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WATCH !!!WATCH !!!
same informationsame information
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Let us watch now the graph of sound Let us watch now the graph of sound pressure variation as a function of time for pressure variation as a function of time for
some real soundssome 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 ?
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WavetoolsWavetools
http://www.physics.mcgill.ca/~grant/225B/http://www.physics.mcgill.ca/~grant/225B/Wavetools/Computerstuff.htmlWavetools/Computerstuff.html
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A very “pure” (but annoying) sound:A very “pure” (but annoying) sound:
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““Musical” sounds (“tones”) are periodicMusical” sounds (“tones”) are periodic
period (T)period (T)
amplitude (A)
frequency (f) = 1/T, T=1/ffrequency (f) = 1/T, T=1/f
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The mathematics of periodic wavesThe mathematics of periodic waves
wavelength: distance between two crests v
vTf
period: time between two crests
Tv
frequency: how many crests per second1 v
fT
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• Period (T) = time for one cycle (measured in s, …)
• Frequency (f) = number of cycles per second (measured in 1/s = Hz)
Example1 1 1
2 0.5 0.52
T s f HzT s s
1 1400 0.0025 2.5
400f Hz T s ms
f Hz
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amplitude = loudnessamplitude = loudness
frequency = pitchfrequency = pitch
shape = timbreshape = timbre
With a few qualifications …
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It is a good time now to read Berg & Stork, It is a good time now to read Berg & Stork,
Chapter 1Chapter 1
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““Pure” tones are sine wavesPure” tones are sine waves
Harmonic oscillatorHarmonic oscillator
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[Using a wave generator, find the lowest and [Using a wave generator, find the lowest and highest audible frequencies and calculate highest audible frequencies and calculate
their period and wavelength]their period and wavelength]
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sin(2 )P A f t
amplitude frequency
phasephase
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How sounds combine: adding two wavesHow sounds combine: adding two waves
300 Hz
450 Hz
300 Hz+
450 Hz
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BeatsBeats
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Tartini tones
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Back to sound (wave) properties …Back to sound (wave) properties …
• reflection
• refraction
• 1/r2 law
• diffraction
• interference
• Doppler effect
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Waves interfere:Waves interfere:
• constructively (amplitudes have the same sign and enhance the wave)
• destructively (amplitudes have opposite sign and partially or completely cancel)
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Interference movieInterference movie
http://www.colorado.edu/physics/2000/schroedinger/big_interference.html
Interference appletInterference applet
http://www.falstad.com/ripple/ex-2source.html
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Doppler effectDoppler effect
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Doppler effect appletDoppler effect applet
http://www.lon-capa.org/~mmp/applist/doppler/http://www.lon-capa.org/~mmp/applist/doppler/d.htmd.htm
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[go to the blackboard and do some real physics][go to the blackboard and do some real physics]
Applications:Applications:
• Doppler radarDoppler radar
• Doppler sonogramDoppler sonogram
• Expansion of the UniverseExpansion of the Universe
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mostly mostly constructive constructive interferenceinterference
mostly mostly destructive destructive interferenceinterference
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•Larger wavelength (~ obstacles) : more diffractionLarger wavelength (~ obstacles) : more diffraction
•Shorter wavelength (<< obstacles) : less diffractionShorter wavelength (<< obstacles) : less diffraction
DiffractionDiffraction
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Ultrasound and sonogramsUltrasound and sonograms
Typical frequencies: 300 MHz
1 1340 0.000001
1300.000.000
mvT v m
f ss
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It is a good time now to read Berg & It is a good time now to read Berg & Stork, Stork,
Chapter 2.4, 2.5, 2.6, 2.7, 2.8, 2.9Chapter 2.4, 2.5, 2.6, 2.7, 2.8, 2.9