Module 1 - Waves, sound and matter

Question 1

Define wave speed

Answer 1

Speed (c) = distance (x) over time (t). Wave speed can be expressed in several different metric units of measurement that denote distance and times. For example km/h and m/s. Wave speed is independent of wavelength (λ) and frequency (f). It is a scalar quantity.

Question 2

Define wave velocity

Answer 2

Velocity describes the speed AND direction of a wave. It is a vector quantity where as speed is a scalar quantity.

Question 3

Define wavelength

Answer 3

It is the physical length of a single cycle. (λ) is measured as a disturbance in space and is the shortest repeat distance and is measured in units of length. Wavelength can be calculated using the formula c = f λ where λ = c/f. If frequency is in Hz and speed is in m/s wavelength will be in meters (m).

Question 4

Define period

Answer 4

It is the time between one cycle and the next. (T) is a measure of disturbance over time and is measured in units of time (s). It can be calculated using the formula T =1/f.

Question 5

Define wave frequency

Answer 5

(f) is measured in hertz (Hz); this used to be called cycles per second (cps). Frequency is the inverse of the period and can be calculated by, manipulating the equation T =1/f to f = 1/T

Question 6

Define wave amplitude

Answer 6

(A) is the maximum variation of pressure from its mean value in the tissues. It has the same units as pressure (Pa or N/m^2). It determines the amount of energy in the US wave.The term amplitude may only be used to refer to a sinusoidal wave. Some people refer to it as magnitude which is far more general. Amplitude refers to the change in pressure that occurs when particles in the wave become rarefied and compressed.

Question 7

Define displacement amplitude

Answer 7

The maximum excursion of an atom from its average position and is usually measured in nanometers (nm = mx10^-9)

Question 8

Outline pressure variation

Answer 8

(p) is measured in the units Pa or Nm^2. po is used to denote ambient pressure. If the pressure is greater than the ambient pressure we say the fluid is compressed (at the crests). If the pressure is less than the ambient pressure we say the fluid is rarefied (at the troughs).

Question 9

Describe pressure variation on an atomic level in a wave

Answer 9

p < po means rarefied. p > po means compressed. So if we compress a region of fluid the atoms within the fluid will become closer together. The interatomic forces will then push these atoms apart. As the atoms expand outward they transfer the compression to their neighbouring atoms and then the original atoms are at a slightly lower pressure. This is how a pressure waves moves at the wave speed. A sound wave in a fluid is a pressure variation with areas of compression and rarefaction.

Question 10

Define volume in terms of US waves

Answer 10

(loudness) is not used in ultrasound. It is determined by the energy of a sound wave. It is related to both pressure amplitude and frequency but as it is zero for sound frequencies used in ultrasound it is not used.

Question 11

Define wave intensity in terms of US waves

Answer 11

(I) The energy carried by a wave over a specific area in a specific time. In ultrasound this is usually expressed as mW/cm2, where 1 mW = 10-3 watt. It is a more precise measurement of the energy of a wave than loudness.

Question 12

Define Power in terms of US waves

Answer 12

The energy content of the beam per second and is closely related to the intensity. The unit of power is the Watt (W). 1 Watt = 1 joule per second.

Question 13

What is the equation used to calculate wave speed, wavelength and frequency

Answer 13

c = f λ

Question 14

What is the frequency range for Ultrasound waves

Answer 14

Approximately 1-15 MHz

Question 15

What are the two different sinusoidal expressions for a wave?

Answer 15

One as a function of disturbance (p) over time (s) where disturbance is the y axis and time is the x axis and period is represented crest to crest. The other is as a function of disturbance (p) over distance (x). Where disturbance is the y axis, distance is the x axis and wavelength is represented crest to crest.

Question 16

Describe a transverse wave

Answer 16

When particles that move do so perpendicular to the direction of wave travel.

Question 17

Describe a longitudinal wave

Answer 17

When particles that move do so parallel to the direction of wave travel. When the particles associated with the material that support the wave vibrate in a direction that is at all times parallel, or antiparallel, to the wave direction.

Question 18

What is wave interference?

Answer 18

Interference occurs when two waves of the same frequency are present in the same region of a material and they interact with each other. The combination of these two waves needs to be calculated to determine the resultant motion of pressure and particle movement. This is done by adding the two wave fronts together.

Question 19

Describe constructive interference

Answer 19

Constructive interference occurs when the crests of two waves occur at the same point. If we had two waves of amplitude A, due to constructive interference the amplitude is now 2A. As power and intensity are directly proportional to amplitude they are now 2^2 = 4.

Question 20

Describe destructive interference

Answer 20

Destructive interference occurs when a crest and a trough of each wave occur at the same point. In this case the resultant amplitude would be 0A, as would the power and intensity.

Question 21

Recite the powers of ten and abbreviations in the SI measurement system.

Answer 21

G, giga = 109 = 1,000,000,000 (a billon)
M, mega = 106 = 1,000,000 (a million)
k, kilo = 103 = 1,000 (a thousand)
h, hecta = 102 = 100 (a hundred)
d, deci = 10-1 = 0.1 = 1/10 (a tenth)
(And not to be confused with deca = 10; ten)
c, centi = 10-2 = 0.01 = 1/100 (a hundredth)
m, milli = 10-3 = 0.001 = 1/1000 (a thousandth)
μ, micro = 10-6 = 0.000001 = 1/1000000 (a millionth)
n, nano = 10-9 = 0.000000001 = 1/1000000000 (a billionth)

Question 22

What, in words, is represented by the symbol A

Answer 22

Amplitude. Units are Pa or N/m^2

Question 23

What, in words, is represented by the symbol λ

Answer 23

Wavelength measured in units of length (mm, cm, m)

Question 24

What, in words, is represented by the symbol f

Answer 24

Frequency Measured in Hertz (Hz)

Question 25

What, in words, is represented by the symbol T

Answer 25

Period Measured in seconds (s)

Question 26

What, in words, is represented by the symbol p

Answer 26

Pressure, disturbance or shape away from the average. Pa or N/m^2

Question 27

What, in words, is represented by the symbol x

Answer 27

Distance measured in units of length (mm, cm, m)

Question 28

What, in words, is represented by the symbol s

Answer 28

Time measured in seconds (s)

Question 29

What is the difference between loudness, intensity and power of a wave?

Answer 29

Loudness - determined by the energy in the sound wave. Not used for ultrasound waves as they have no sound and are zero.
Intensity – Determined by the energy of a sound wave. Used for ultrasound as it is more precise and removes the element of human perception that loudness has. It is the energy carried by the wave covering some specified area in a specified time . Expressed as mW/cm2
Power (P) - the energy content of the beam per second. Unit is the watt. Watt = 1 joule per second, or 1 J/s

Question 30

What are three examples of transverse waves and longitudinal waves.

Answer 30

All stringed instruments have transverse vibrations of the strings (piano, violin, guitar etc.).Ocean waves, jerking a rope
All wind instruments have longitudinal waves set up in a column of air (flute, trumpet, saxophone, etc.). sound waves, ultrasound waves, seismic p-waves

Question 31

What sort of waves are sound waves in fluid?

Answer 31

Longitudinal

Question 32

What is the average speed of ultrasound in soft tissue?

Answer 32

1540m/s

Question 33

What are the typical wavelengths and frequency of audible sound waves?

Answer 33

The audible sound range for humans is from about 50Hz to 20 000Hz and the speed of sound in air is 330. Ultrasound has much higher frequencies and as such, much shorter wavelengths.
So if c = f λ λ=c/f
λ = 330/50 = 6.6m = 6.6x10^3mm
& 330/20 000 = 0.0165m = 16.5mm
So wavelength of audible sound vary roughly from 16.5 to 6.6x10^3mm

Question 34

Describe the nature of propagation of sound

Answer 34

A sound wave is a pressure wave comprised of areas of compression and rarefaction of the particles that make up the material. A sound wave requires a material to support it. It can travel in fluids and solids. A travelling wave transmits energy but not the particles the material is made up of. In a fluid, sound waves are longitudinal (where the particles vibrate in the same direction as the propagation of the wave). The material the sound wave is travelling through is what determines wave speed not the frequency or wavelength.

Question 35

Describe the longitudinal nature of a sound wave in a fluid

Answer 35

A longitudinal soundwave is a wave whose transmitted energy travels in the same direction that the particles of the material that support it are vibrating. It is a pressure wave that is comprised of areas of compression and rarefaction. When drawn as a sinusoidal wave the crests represent areas of compression and the troughs, areas of rarefaction. The energy is transported due to the nature of atomic properties. As a point of the fluid is acted upon by the sound wave the atoms of the molecules in this area are compressed together. It is in the atoms nature to the push away from each other and as they push away from the source they compress the area immediately near them and so on and so forth.

Question 36

Differentiate between the terms speed and velocity of an ultrasound wave

Answer 36

Speed denotes the speed at which the wave transmits energy through a material and is a scalar quantity. Velocity denotes the speed AND direction the wave transmits energy and is a vector quantity.

Question 37

What is the speed of ultrasound in soft tissue and by how much does it vary?

Answer 37

The speed of ultrasound in soft tissue is approximately 1540m/s. This varies +/-10%.

Question 38

What is meant by the density, ρ, of tissue?

Answer 38

Density is the measure of a materials mass per unit volume. ρ = m/V. measured in kg/m^3 and cm/g^3

Question 39

What is meant by bulk modulus, β, of tissue?

Answer 39

Bulk Modulus, is a measure of how resistant a material is to compression. The measure of a decrease in volume due to an increase in pressure also known as a materials stiffness.
Is the ratio of the change in pressure to the corresponding fractional change in volume (This relates to the compressibility of the material)

Question 40

What is acoustic impedance in relation to US in soft tissue?

Answer 40

A measure of how difficult it is to transmit a sound wave through a given medium, overcoming the stiffness of the material and the inertia of the vibrating particles (density). It can be expressed by the equation Z = ρ x c.
The units of acoustic impedance are kg/m2/

Question 41

What is an acoustic interface?

Answer 41

The boundary between two materials with different acoustic impedances. In this way, tissue interface means a change of acoustic impedance.

Question 42

What is specular reflection?

Answer 42

Specular reflection – Or reflection. Occurs when a sound wave is incident on an acoustic interface and some of it is reflected. The law of reflection states that the angle of incidence (θi) will be equal to the angle of reflection (θr). The angles are measured against the normal.

Question 43

How do you calculate the reflection coefficient and what are it’s conditions?

Answer 43

R = Ir/Ii = (Z2 – Z1)^2/(Z2 + Z1)^2
The reflection coefficient, R, is the intensity of the reflected wave, Ir, divided by the intensity of the incident wave, Ii, and is determined by the acoustic impedances of the two media comprising the interface. This equation only applies when the beam has normal incidence on an interface.

Question 44

What is scattering?

Answer 44

A general term that simply describes the phenomenon of a wave changing its direction. It can be reflected, refracted, scattered and diffracted. The word scattering can also refer to the interaction of ultrasound with small structures (such as red cells and capillaries). It differs from reflection in two different ways.

1) scattered energy is distributed in all directions where as reflected ultrasound goes in a single direction.
2) Scattered energy is generally much weaker so the echoes are much weaker and displayed as low to mid level grey tones.

Question 45

What is backscatter?

Answer 45

Scatter in approximately the opposite direction to the incident wave.

Question 46

What is refraction?

Answer 46

Along with reflection, occur when a wave interacts with an acoustic interface. The component of the incident wave that is not reflected is refracted (or transmitted) as it travels through the acoustic interface. The refracted wave travels through the second medium but usually in a different direction to the incident beam. The exception is when the incident beam is 90 degrees. This is governed by the law of refraction, or Snell’s Law.

Question 47

How do you calculate the transmission coefficient and what are it’s conditions?

Answer 47

T = It/Ii = 4Z2 Z1 /(Z2 + Z1)2
Similar to the reflection coefficient, the transmission (refraction) coefficient, T, is the intensity of the transmitted wave, It, divided by the intensity of the incident wave, Ii This equation only applies when the beam has normal incidence on an interface.
R + T = 1 so T = 1-R and vice versa.

Question 48

What is the critical angle?

Answer 48

The angle of incidence for which the angle of refraction is 90 degrees. It only occurs if the propagation speed is higher in the second tissues than the first. If the incident angle is greater than the critical angle, total reflection occurs. Snell’s law yields the following equation for the critical angle, θc:-
sin(θc) = c1/c2

Question 49

What is Snells law?

Answer 49

Snell’s Law – relates the angles of Incidence (θi) and refraction (θf). [sin(θi) / sin(θf)] = ci / cf

Question 50

What are the two separate mechanisms of causing total reflection?

Answer 50

When there is a very large difference in the acoustic impedance of the two tissues.
When propagation speed in the second tissues is higher and the incident angle exceeds the critical angle.

Question 51

What is attenuation?

Answer 51

is the decrease in energy of the wave as measured in the direction of the incident wave due to both absorption and all forms of scattering.

Question 52

What are the mathematical expressions of attenuation?

Answer 52

It can be expressed quantitatively as attenuation = absorption + scatter.

Question 53

What is absorption?

Answer 53

Wave energy that is absorbed and converted to heat.

Question 54

Differentiate between the terms speed and velocity for a wave, and indicate the importance of each.

Answer 54

Speed refers to the speed of the wave and does not consider the direction. It is therefore a scalar quantity.
Velocity is wave speed and the direction in which the wave is travelling. It is therefore a vector quantity.

Question 55

What is the average sound wave speed assumed in human soft tissue? By how much, approximately, does this vary for various soft tissue types?

Answer 55

The average sound wave speed assumed in human soft tissue is 1540m/s. This varies approximately +/- 10% for various soft tissue types.

Question 56

List all possible sound wave/tissue interactions that involve the wave changing its direction upon interaction.

Answer 56

Reflection, refraction, diffraction and back scatter.

Question 57

What do we mean by the normal at an interface? What is the significance of the normal in reflection and refraction?

Answer 57

The normal is perpendicular to the interface. The normal is significant when considering reflection and refraction as the angles of each are measured against the normal.

Question 58

Consider the typical wavelength of an ultrasound wave, say with a frequency of 10 MHz, and think of what soft tissue structures and organs might have dimensions (sizes) much greater than the wavelength and those that might have dimensions much smaller than the wavelength.

Answer 58

c = fλ λ= c/f = 1540/10^6 = 0.15mm
Almost all soft tissue structures and organs are bigger than this. Bone, muscle, tendons. Structures smaller than this include blood and micro bubbles of air.

Particulate matter in blood or urine

Question 59

What is the pulse echo principle?

Answer 59

By carefully measuring the time between the transmission of a transmit pulse and the reception of a given echo, the ultrasound machine can calculate the distance between the probe and the structure that caused the echo.
Velocity, c = distance / time = 2 x D / ▲t
Where D is the depth of the structure. As we use the constant velocity of 1540m/s in soft tissue and we can measure the elapsed time we can determine the approximate depth of structures.
The average velocity of sound in soft tissue is 1540m/s or 154000cm/s hence the formula can be rearranged for D
D = 154000 x ▲t / 2
The information is used by the machine to form an image

Question 60

Of all the wave-matter interactions can you suggest the most important in B-mode ultrasound imaging?

Answer 60

Back scatter as it is what forms the image.

Question 61

What is the emit receive cycle and why is it important?

Answer 61

The emit receive cycle is necessary for the pulse echo principle to work and the ultrasound machine to form an image. The imaging transducer will emit a pulse and wait to receive an echo before emitting another pulse. This is so that elapsed time can be accurately measured.

Question 62

What is the Pulse Repetition Period (PRP)?

Answer 62

The time between emitting pulses. It must allow time for the pulse to reach maximum depth (Dmax) and return.
It is inversely related to the PRF. Just like T = 1/f
PRP = 1/PRF

Question 63

What is the Pulse Repetition Frequency (PRF)?

Answer 63

It is the term used to describe the number of transmit pulses each second. Is inversely related to the PRP. Just like f = 1/T
PRF = 1 / PRP

Question 64

Explain the difference between frequency and pulse repetition frequency.

Answer 64

Pulse repetition frequency is the is the frequency of the emit receive cycle, measured in cps or cycles per second. Wave frequency is measured in Hz, however used to be measured in cps. It refers to the frequency of the wave itself rather than the frequency of the emit receive cycle.

Question 65

What are the physical processes that give rise to wave attenuation in terms of absorption and scatter, in all its forms.

Answer 65

Attenuation of an ultrasound beam depends on the tissue the wave is travelling in as well as it’s frequency. The dependency on frequency is important to remember as the beam is more readily attenuated when it has a high frequency.
The deeper the structure the lower the frequency needs to be as the more tissue it has to travel through the more it is attenuated.

Question 66

What is the average attenuation of the US beam in soft tissue?

Answer 66

0.7 dB/cm/MHz (strictly should be written 1 dB/cm-MHz)

It is approximate but is assumed to express both the absorption and scatter parts of attenuation.

Question 67

What is the basic relationships between the amplitude and intensity of a wave.

Answer 67

Intensity and Amplitude, I and A, are related by
I = const. A2
So, if a decrease by a factor of three I will decrease by a factor of 9.
I = const. 3^2 = 9

Question 68

What is the equation used to calculate attenuation in decibels using two intensity values?

Answer 68

dB = 10 log10 (Ix/Io) (4.3)
In the intensity ratio “inside” the logarithm function of Equation (4.3), the denominator is the intensity of the ultrasound wave at the “initial” position or time (Io ), the numerator is the intensity of the wave at the “final” position or time (Ix )

Question 69

What is the equation used to calculate attenuation in decibels using two amplitude values?

Answer 69

dB = 10 log10(Ax/Ao)2 = 20 log10 (Ax/Ao) Equation (4.4)
In the amplitude ratio the denominator is the amplitude of the ultrasound wave at the “initial” position or time (Ao ), the numerator is the amplitude of the wave at the “final” position or time.( Ax )

Question 70

What do positive and negative dB values mean in terms of intensity?

Answer 70

A positive dB value means the intensity (energy) is increasing (Ix > I0) while a negative dB value means the intensity is decreasing (Ix < I0).

Question 71

What does and increase or decease of dB 3 mean?

Answer 71

So -3 dB means the intensity has halved. In a similar way, +3 dB means the intensity has doubled. By the same kind of process you can easily show that

   - 6 dB means Ix/I0 = 0.25 = 1/4 = (1/2)2
   - 9 dB means Ix/I0 = 0.125 = 1/8 = (1/2)3

with every drop by 3 dB indicating another further halving of the intensity, or energy or power.

Question 72

What will happen if you enter the intensity ratio back the front when calculating attenuation in decibels?

Answer 72

In using the dB expression, the ratio inside the log10 function is usually arranged with the initial (or reference) intensity value in the denominator (bottom) and the final intensity value in the numerator (top). If you inadvertently get the ratio the other way around, the result will have the same value magnitude with the opposite sign.

Question 73

What is the average value of the way the ultrasound beam intensity changes as it travels through tissue?

Answer 73

0.7 dB/cm/MHz

Question 74

What is the equation for estimating attenuation loss in soft tissue?

Answer 74

Attenuation loss = 0.7 x f x 2D dB

Where f is frequency in MHz and D is depth in cm

Question 75

What is the equation that can be used to calculate maximum gain and rearranged to calculate maximum maximum field of view for a transducer of a given frequency?

Answer 75

Maximum gain = 0.7 x f x 2 Dmax

Where f is frequency in MHz and D max is maximum field of view given f in cm and maximum gain is in dB.

Question 76

What are the three important equations to remember when calculating the dB change from emitted to received ultrasound wave due to both attenuation and reflection ?

Answer 76

The reflection coefficient
R = Ir/Ii = [(Z1 - Z2)/(Z1 + Z2)]2

This intensity decrease in the reflected wave at the interface can be expressed in dB, as;

Reflective loss = 10 log (Ir/Ii) = 10 log R
Ir = reflected intensity Ii = incident intensity

Hence the total difference between the emitted and returning ultrasound intensity:

Total intensity loss = (0.7 x 2 x D x f) + 10 log R
Where d is depth in cm, f is the frequency of the given transducer in MHz and R is the reflection coefficient.