Human Hearing Physics 111 Lecture 30 (Walker: 14.4-6)

Human Hearing & Sound Perception Doppler Effect

Nov. 20, 2009

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Frequency Range of Human Hearing

0 20 Hz 20 kHz Audible (Audio) Frequencies Infrasonic Ultrasonic

The ear perceives the pitch of a sound from Threshold of the repetition frequency, or fundamental frequency, of the waveform Hearing: ∆P=2x10-5 Pa 10 (Patm/10 ) Lecture 30 7/32 Lecture 30 8/32 The Ear and its Response; Loudness Audiogram - Chart of Hearing Loss The ear’s sensitivity varies with frequency. These curves translate the intensity into sound level at different frequencies.

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Fundamental Frequency Range Waveforms & Sound “Quality” of Musical Instruments •The waveform of a sound wave is the pattern of air pressure changes over one cycle Piccolo Sine Wave: Soprano Perceived as a “pure Voice tone”. Excites only Bass one region of the Voice Basilar Membrane Piano Triangle Wave: Perceived Freq (Hz) 27.5 82 131 262 523 1046 2093 4186 as “complex tone”. Pitch A E C C C C C C Excites several areas of 2 3 4 5 6 7 8 Basilar Membrane. Can Note(!) that going up an octave in pitch doubles frequency be made by combining sine wave “building blocks”. Lecture 30 11/32 Lecture 30 12/32 Musical Waveforms 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 Tuning Fork Clarinet Cornet • Compare to the situation of “complex light” such as white light, which is made Demonstration – Listen to & see some waveforms up of a mixture of the “pure” colors of the rainbow

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Lecture 30 15/32 Lecture 30 16/32 Musical “Tone Quality” Harmonics • Complex music tones (waveforms) built up from: (Timbre) –A fundamental sine wave (frequency f) • Tone quality, or timbre, is determined – Harmonics of the fundamental – i.e., sine waves whose frequencies are integer multiples of the by the waveform, or alternately, by the fundamental frequency f spectrum or harmonic content of the •2nd harmonic: sine wave of frequency 2f sound. •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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Lecture 30 19/32 Lecture 30 20/32 Doppler Effect Doppler Effect: Moving Observer • Change in observed frequency when source For an observer moving at speed u towards a and observer are in relative motion stationary source, observed frequency f’ is: • A. Fixed Source; Moving Observer ⎛ u ⎞ f ′ = ⎜1+ ⎟ f ⎝ v ⎠ Observed frequency and pitch shifted higher. If observer moving away at speed u: ⎛ u ⎞ f ′ = ⎜1− ⎟ f ⎝ v ⎠ Observed frequency and pitch shifted lower. Lecture 30 21/32

To summarize, for observer moving at speed u: 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? ⎛ u ⎞ f ′ = ⎜1+ ⎟ f ⎝ v ⎠ Top sign for observer moving toward source; bottom sign for observer moving away. ⎛ 20m / s ⎞ Speed of sound is v. f ′ = ⎜1+ ⎟500Hz = 529 Hz ⎝ 343m / s ⎠

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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 Effect: Moving Source Example: Moving Source For a source moving at speed u • 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? ⎛ 1 ⎞ f '= ⎜ ⎟ f ⎝1− u / v ⎠ Top sign for source moving toward observer ⎛ 1 ⎞ (observed frequency shifted up; bottom sign = ⎜ ⎟500Hz = 531 Hz for source moving away from observer ⎝1− 20 / 343⎠ (observed frequency shifted down). Speed of sound is v. Lecture 30 27/32 Lecture 30 28/32 Doppler Effect: Source & Doppler Applications Observer Moving At left, a Doppler radar shows the hook echo characteristic of tornado formation. At right, a Doppler blood flow speed meter.

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). Lecture 30 29/32 Lecture 30 30/32

Doppler Bloodflow Measurement • E.g., “Doppler blood flow End of Lecture 30 velocity waveforms in the fetal renal artery” • For Monday, Nov. 30, read Walker 14.7-8. (Archives of Gynecology and Obstetrics) • Homework Assignment 14b is due at 11:00 PM on • Fetal Doppler Heart Sunday, Nov. 29. Monitor Specifications: Heart Rate Range 50- 240 Bpm Ultrasound Frequency 2 MHz

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