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Lecture 30 1/32
Physics 111Lecture 30 (Walker: 14.4-6)
Human Hearing & Sound PerceptionDoppler Effect
Nov. 20, 2009
Lecture 30 2/32
Human Hearing
Lecture 30 3/32 Lecture 30 4/32
Lecture 30 5/32 Lecture 30 6/32
Lecture 30 7/32
Frequency Range of Human Hearing
0 20 Hz 20 kHz
Audible (Audio) FrequenciesInfrasonic Ultrasonic
The ear perceives the pitch of a sound from the repetition frequency, or fundamental frequency, of the waveform
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Threshold of Hearing: ∆P=2x10-5 Pa(Patm/1010)
The Ear and its Response; LoudnessThe ear’s sensitivity varies with frequency. These curves translate the intensity into sound level at different frequencies.
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Audiogram - Chart of Hearing Loss
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Fundamental Frequency Range of Musical Instruments
Freq (Hz) 27.5 82 131 262 523 1046 2093 4186Pitch A E2 C3 C4 C5 C6 C7 C8
Note(!) that going up an octave in pitch doubles frequency
Piano
BassVoice
SopranoVoice
Piccolo
Lecture 30 12/32
Waveforms & Sound “Quality”• The waveform of a sound wave is the pattern
of air pressure changes over one cycle
Sine Wave:Perceived as a “pure tone”. Excites only one region of the Basilar Membrane
Triangle Wave: Perceived as “complex tone”. Excites several areas of Basilar Membrane. Can be made by combining sine wave “building blocks”.
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Musical Waveforms
Tuning Fork Clarinet Cornet
Demonstration – Listen to & see some waveforms
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Waveform Spectrum (Harmonics)• Complex tones (triangle wave, clarinet
waveform) can be made by combining sine waves with different frequencies.
• The sine wave frequencies used, and the amount of each, determine the spectrum of the waveform
• Compare to the situation of “complex light” such as white light, which is made up of a mixture of the “pure” colors of the rainbow
Lecture 30 15/32 Lecture 30 16/32
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Musical “Tone Quality”(Timbre)
• Tone quality, or timbre, is determined by the waveform, or alternately, by the spectrum or harmonic content of the sound.
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Harmonics• Complex music tones (waveforms) built up from:
– A fundamental sine wave (frequency f)– Harmonics of the fundamental – i.e., sine waves
whose frequencies are integer multiples of the fundamental frequency f• 2nd harmonic: sine wave of frequency 2f• 3rd harmonic: sine wave of frequency 3f, etc.
• For example, “A above middle C” on a cornet has– 3 units 440 Hz sine wave (fundamental)– 4.5 units 880 Hz sine (2nd harmonic)– 8 units 1320 Hz sine (3rd harmonic)– 3 units 1760 Hz sine (4th harmonic), etc.
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Doppler Effect• Change in observed frequency when source
and observer are in relative motion• A. Fixed Source; Moving Observer
Doppler Effect: Moving ObserverFor an observer moving at speed u towards a stationary source, observed frequency f’ is:
Observed frequency and pitch shifted higher.
If observer moving away at speed u:
fvuf ⎟⎠⎞
⎜⎝⎛ +=′ 1
fvuf ⎟⎠⎞
⎜⎝⎛ −=′ 1
Observed frequency and pitch shifted lower.
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To summarize, for observer moving at speed u:
Top sign for observer moving toward source; bottom sign for observer moving away. Speed of sound is v.
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Example• Fixed siren putting out sound wave of
frequency 500 Hz. You drive toward it at a speed of 20 m/s. What frequency do you hear?
Hzsmsmf 500/343/201 ⎟
⎠⎞
⎜⎝⎛ +=′
fvuf ⎟⎠⎞
⎜⎝⎛ +=′ 1
= 529 Hz
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The Doppler Effect - Moving Source, Fixed Observer
The Doppler effect from a moving source can be analyzed similarly; now it is the wavelength that appears to change:
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Doppler Shift – Moving Source
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Doppler Effect: Moving SourceFor a source moving at speed u
Top sign for source moving toward observer (observed frequency shifted up; bottom sign for source moving away from observer (observed frequency shifted down). Speed of sound is v.
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Example: Moving Source• Siren on police car putting out sound wave of
frequency 500 Hz. Car is driving toward you at a speed of 20 m/s. What frequency do you hear?
= 531 HzHz
fvu
f
500343/201
1/1
1'
⎟⎠⎞
⎜⎝⎛−
=
⎟⎠⎞
⎜⎝⎛−
=
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Doppler Effect: Source & Observer Moving
Top signs for source and observer moving toward each other (observed frequency shifted up; bottom sign for source and observer moving away from each other (observed frequency shifted down).
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Doppler Applications
At left, a Doppler radar shows the hook echo characteristic of tornado formation. At right, a Doppler blood flow speed meter.
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Doppler Bloodflow Measurement• E.g., “Doppler blood flow
velocity waveforms in the fetal renal artery”(Archives of Gynecology and Obstetrics)
• Fetal Doppler Heart Monitor Specifications:Heart Rate Range 50-240 BpmUltrasound Frequency 2 MHz
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End of Lecture 30• For Monday, Nov. 30, read Walker 14.7-8.
• Homework Assignment 14b is due at 11:00 PM on Sunday, Nov. 29.