Resident Physics Lectures

1
Resident Physics Lectures

• 02
• Sound Properties and Parameters

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Sound Wave Definition?

• Sound is a Wave
• Wave is a propagating (traveling) variation in a
  wave variable
• An elephant is big, gray, and looks like an
  elephant.

3
Sound Wave Variable

• Examples
• pressure (force / area)
• density (mass / volume)
• temperature
• Also called acoustic variable

Sound is a propagating (moving) variation in a
wave variable
4
Sound Wave Variation

• Freeze time
• Measure some acoustic variable as a function of
  position

Pressure Density Temperature
Acoustic Variable Value
Position
5
MORE

• Make many measurements of an acoustic variable an
  instant apart
• Results would look the same but appear to move in
  space

1
Instant 1
Instant 2
2
6
MORE

• Track acoustic variable at one position over time

7
Sound Waves

• Waves transmit energy
• Waves do not transmit matter
• Crowd wave at sports event
• peoples elevation varies with time
• variation in elevation moves around stadium
• people do not move around stadium

8
Transverse Waves

• Particle moves perpendicular to wave travel
• Water ripple
• surface height varies with time
• peak height moves outward
• water does not move outward

9
Compression (Longitudinal) Waves

• Particle motion parallel to direction of wave
  travel

1
1
Motion ofIndividual Coil
2
2
Wave Travel
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Sound Waves are Compression Waves

• Regions of alternating low and high pressure move
  through air
• Particles oscillate back forth parallel to
  direction of sound travel
• Particles do not move length of sound wave

Wave Travel
Motion of IndividualAir Molecule
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Medium

• Material through which wave moves
• Medium not required for all wave types
• no medium required for electromagnetic waves
• radio
• x-rays
• infrared
• ultraviolet
• medium is required for sound
• sound does not travel through vacuum

Talk louder! I cant hear you.
12
Sound Waves

• Information may be encoded in wave energy
• radio
• TV
• ultrasound
• audible sound

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Sound Frequency

• light frequency corresponds to color
• sound frequency corresponds to pitch

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Sound Frequency

• of complete variations (cycles) of an acoustic
  variable per unit time
• Units
• cycles per second
• 1 Hz 1 cycle per second
• 1 kHz 1000 cycles per second
• 1 MHz 1,000,000 cycles per second
• Human hearing range
• 20 - 20,000 Hz

15
Sound Frequency

• Ultrasound definition
• gt 20,000 Hz
• not audible to humans
• dog whistles are in this range
• Clinical ultrasound frequency range
• 1 - 10 MHz
• 1,000,000 - 10,000,000 Hz

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Period

• time between a given point in one cycle the
  same point in the next cycle
• time of single cycle
• Units
• time per cycle (sometimes expressed only as time
  cycle implied)

Magnitude of acoustic variable
period
time
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Period
1 Period
------------------- Frequency

• as frequency increases, period decreases
• if frequency in Hz, period in seconds/cycle

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Period
Period 1 / Frequency

• if frequency in kHz, period in msec/cycle
• if frequency in MHz, period in msec/cycle
• 1 kHz frequency gt 1 msec period
• 1 MHz frequency gt 1 msec period

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Reciprocal Units
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Period / Frequency
If frequency 2 MHz then sound period is 1/2
0.5 msec
If frequency 10 kHz then sound period is 1/10
0.1 msec
If frequency 50 Hz then sound period is 1/50
0.02 sec
If sound period 0.2 msec then frequency 1/0.2
5 MHz
If sound period 0.4 msec then frequency 1/0.4
2.5 kHz
If sound period 0.1 sec then frequency 1/0.1
10 Hz
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Sound Period Frequency are determined only by
the sound source. They are independent of medium.
Who am I?
Burt Mustin
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Propagation Speed

• Speed only a function of medium
• Speed virtually constant with respect to
  frequency over clincial range

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Wavelength

• distance in space over which single cycle occurs
  OR
• distance between a given point in a cycle
  corresponding point in next cycle
• imagine freezing time, measuring between
  corresponding points in space between adjacent
  cycles

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Wavelength Units

• length per cycle
• sometimes just length cycle implied
• usually in millimeters or fractions of a
  millimeter for clinical ultrasound

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Wavelength Equation

• Speed Wavelength X Frequency
  c l X n (dist./time) (dist./cycle)
  (cycles/time)
• As frequency increases, wavelength decreases
• because speed is constant

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Wavelength

• Speed Wavelength X Frequency
  c l X n (dist./time) (dist./cycle)
  (cycles/time)
• mm/msec mm/cycle
  MHzCalculate Wavelength for 5 MHz sound
  in soft tissue

Wavelength 1.54 mm/msec / 5 MHz
5 MHz 5,000,000 cycles / sec 5 cycles / msec
Wavelength 1.54 / 5 0.31 mm / cycle
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Wavelength is a function of both the sound source
and the medium!
Who am I?
John Fiedler
28
Pulsed Sound

• For imaging ultrasound, sound is
• Not continuous
• Pulsed on off
• On Cycle (speak)
• Transducer produces short duration sound
• Off Cycle (listen)
• Transducer receives echoes
• Very long duration

ON
OFF
ON
OFF
(not to scale)
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Pulse Cycle

• Consists of
• short sound transmission
• long silence period or dead time
• echoes received during silence
• same transducer used for
• transmitting sound
• receiving echoes

sound
sound
silence
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Pulsed Sound Example

• ringing telephone
• ringing tone switched on off
• Phone rings with a particular pitch
• sound frequency

sound
sound
silence
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Parameters
Sound
Pulse

• pulse repetition frequency
• pulse repetition period
• pulse duration
• duty factor
• spatial pulse length
• cycles per pulse

• frequency
• period
• wavelength
• propagation speed

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Pulse Repetition Frequency

• of sound pulses per unit time
• of times ultrasound beam turned on off per
  unit time
• independent of sound frequency
• determined by source
• clinical range (typical values)
• 1 - 10 KHz

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Pulse Repetition Period

• time from beginning of one pulse until beginning
  of next
• time between corresponding points of adjacent
  pulses

Pulse Repetition Period
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Pulse Repetition Period

• Pulse repetition period is reciprocal of pulse
  repetition frequency
• as pulse repetition frequency increases, pulse
  repetition period decreases
• units
• time per pulse cycle (sometimes simplified to
  just time)
• pulse repetition period frequency determined by
  source

PRF 1 / PRP
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Pulsed Sound

• Pulse repetition frequency period independent
  sound frequency period

Same FrequencyHigher PulseRepetition Frequency
Higher FrequencySame PulseRepetition Frequency
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Pulse Duration

• Length of time for each sound pulse
• one pulse cycle
• one sound pulse and one period of
  silence
• Pulse duration independent of duration of silence

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Pulse Duration

• units
• time per pulse (time/pulse)
• equation
• pulse duration Period X cycles per
  pulse(time/pulse) (cycles/pulse)
  (time/cycle)

Pulse Duration
Period
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Pulse Duration
Longer Pulse Duration
Same frequency pulse repetition
frequency, period, pulse repetition period
Shorter Pulse Duration
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Pulse Duration
Pulse duration is a controlled by the sound
source, whatever that means.
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Duty Factor

• Fraction of time sound generated
• Determined by source
• Units
• none (unitless)
• Equations

Duty Factor Pulse Duration / Pulse Repetition
Period
Duty Factor Pulse Duration X Pulse Repetition
Freq.
Pulse Duration
Pulse Repetition Period
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Spatial Pulse Length

• distance in space traveled by ultrasound during
  one pulse

H.......E.......Y
HEY
Spatial Pulse Length
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Spatial Pulse Length
So, can you like show me an example?
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Spatial Pulse Length
Equation
Spat. Pulse Length cycles per pulse X
wavelength
(dist. / pulse)
(cycles / pulse) (dist. / cycle)

• depends on source medium
• as wavelength increases, spatial pulse length
  increases

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Spatial Pulse Length
Spat. Pulse Length cycles per pulse X
wavelength
Wavelength Speed / Frequency

• as cycles per pulse increases, spatial pulse
  length increases
• as frequency increases, wavelength decreases
  spatial pulse length decreases
• speed stays constant

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Why is Spatial Pulse Length Important
Spat. Pulse Length cycles per pulse X
wavelength
Wavelength Speed / Frequency
Spatial pulse length determines axial resolution
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Acoustic Impedance

• Definition
• Acoustic Impedance Density X Prop.
  Speed(rayls) (kg/m3)
  (m/sec)
• increases with higher
• Density
• Stiffness
• propagation speed
• independent of frequency

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Why is Acoustic Impedance Important?

• Definition
• Acoustic Impedance Density X Prop.
  Speed(rayls) (kg/m3)
  (m/sec)
• Differences in acoustic impedance determine
  fraction of intensity echoed at an interface