Ultrasound Physics & Instrumentation
4th Edition
Volume I
Companion Presentation
Frank R. Miele
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Volume I Outline
 Chapter 1: Mathematics
 Chapter 2: Waves
 Level 1
 Level 2
 Chapter 3: Attenuation
 Chapter 4: Pulsed Wave
 Chapter 5: Transducers
 Chapter 6: System Operation
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Chapter 2: Waves - Level 2
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Classification of Sound
Notice how the same data is
presented on both a linear
and a logarithmic scale.
Because of the large dynamic
range, notice that the
logarithmic scale is a more
“useful” way of presenting the
data.
Fig. 26: Linear and Logarithmic Scale (Pg 112)
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Sound Ranges
0.02
0.2
Infrasound
2
Note that:
20
 “infra” means below
200
 “ultra” means above
Audible Range
 “audible” refers to human hearing
2K
20 K
200 K
2M
Ultrasound
Diagnostic Ultrasound
20 M
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Typical Ultrasound Periods
The frequency and the period give the same information.
You should be able to convert back and forth between the period and
the frequency.
 Frequency = 2 MHz
 Period = 1/(2 MHz) = 0.5 sec
 Frequency = 10 MHz

Period = 1/(10 MHz) = 0.1  sec
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Diagnostic Ultrasound and Higher
Frequencies
Fig. 27: Intravascular Ultrasound (IVUS) Image of a Coronary Artery (Pg 113)
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Propagation Velocity (c)
In Level 1, we discussed the fact that sound was determined strictly by the
properties of the medium. It is now important to discuss which properties of the
medium affect the propagation velocity and how.
 The propagation velocity is related to the square root of the bulk
modulus of the medium.
 The propagation velocity is inversely related to the density of the
medium.
 modulus
c

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Bulk Modulus
Bulk Modulus 
Fig. 28: Changing Volume with
Pressure (Pg115)
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stress  Pr essure

strain  Volume 


 Volume 
Bulk Modulus and Stiffness
High Bulk Modulus results when the material is stiff (incompressible or
inelastic). Therefore, materials that are stiff tend to have high
propagation speeds.
Propagation Speed (c) is related to stiffness.
(stiffer mediums have higher propagation speeds)
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Propagation Velocity Analogy
Fig. 29:
(Pg 116)
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Stiffness and Propagation Velocity
Slower Wave
Propagation
(More Compressible)
Faster Wave
Propagation
(Stiffer)
Fig. 30: (Pg 117)
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Compressibility and Propagation Velocity
(Animation)
(Pg. 118 A)
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Density and Propagation Velocity
Slower Wave
Propagation
(Higher Density)
Faster Wave
Propagation
(Lower Density)
Fig. 31: (Pg 117)
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Density and Propagation Velocity
(Animation)
(Pg. 118 B)
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Wave Velocity versus Train Velocity
Fig. 32:
(Pg 118)
Notice that the “wave” moves 30 m in the time that the train only moved 3 m.
(See animation of next slide)
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Wave vs. Train Velocity (Animation)
(Pg. 118 C)
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Don’t Oversimplify
 At first glance, it appears that higher density materials would have lower
propagation velocities because of the inverse relationship.
 This contradicts what we see in reality in the body.
 The reason is that the bulk modulus is generally higher for more dense
materials (it is harder to compress a dense material than a less dense
material).
 A higher bulk modulus results in a higher propagation velocity.
 Therefore, more dense materials in the body tend to have higher not lower
propagation velocities.
This last fact becomes apparent by looking at the table of propagation velocities.
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Propagation Velocities in the Body
Medium
Propagation Velocity
Air (25 degrees C)
347 m/sec
Lung
500 m/sec
Fat
1440 m/sec
Water (25 degrees C)
1495 m/sec
Brain
1510 m/sec
“Soft Tissue”
Average 1540 m/sec
Liver
1560 m/sec
Kidney
1560 m/sec
Blood
1560 m/sec
Muscle
1570 m/sec
Bone
4080 m/sec
Table 5: (Pg 121)
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Propagation Speed (c) Summary
The propagation speed of sound is determined by two properties of the medium:
 density ()
 (Bulk Modulus) stiffness
As the density increases, the propagation speed decreases.
(assumes no change in stiffness – which is not very realistic)
As the stiffness increases the propagation speed increases.
Important point: For most materials, as the density increases, the
stiffness increases much faster. This non-linear relationship results in
more dense materials typically having much higher propagation
velocities.
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Density, Stiffness and Propagation
Velocity (Animation)
(Pg. 119)
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Calculating the Wavelength
You must be able to calculate the wavelength. (Pages 123 - 124)
Example: If the transmit frequency is 5 MHz, what is the wavelength
in water?
f  5 MHz
c  1495
m
sec
 ?
m
c
m
sec  1500
 
 3 m
1
f
5 MHz
5 M
 sec 
sec
1495
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Power
Power is a measure of how much work or energy is expended per time.
Power has units of Watts.
Power  Amplitude
2
So what happens to the power if you double the transmit voltage
(amplitude)?
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Intensity
The intensity is the distribution of power over area.
Intensity has units of Watts per area:
Power
Intensity 
area
So what happens to the intensity if you double the transmit voltage
(amplitude)?
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Relationship of intensity with Amplitude
Power  Amplitude 
Intensity 

area
area
2
So if the amplitude is doubled, the power increases by a factor
of four, resulting in an increase in intensity by a factor of four.
Recall that voltage is a measure of amplitude.
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Decibels
Decibels is a logarithmic power ratio:
Power form :
Amplitude form :
 Pf 
dB
10  log  
 Pi 
Where :
 Af 
dB
20  log  
 Ai 
Where :
Pf  power final
Af  amplitude final
Pi  power initial
Ai  amplitude initial
Note: the extra factor of 2 in the amplitude form converts the amplitude
ratio into a power ratio.
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Amplitude versus Frequency
Amplitude and frequency are measures of completely different parameters.
In terms of sound:
 Amplitude corresponds to volume
 Frequency corresponds to pitch
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Same Frequency – Different Amplitude
Fig. 33:
(Pg 135)
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Same Amplitude – Different Frequency
Fig. 34:
(Pg 136)
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