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Physics 111Lecture 30 (Walker: 14.4-6)

Human Hearing & Sound PerceptionDoppler Effect

Nov. 20, 2009

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Human Hearing

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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

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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

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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.