Chapter 6: Wave phenomena

Question 1

characteristic acoustic impedance is calculated how? (z)

Answer 1

z=pc

Question 2

nonlinearity parameter is also called

Answer 2

B/A

Question 3

Continuity of pressure is what?

Answer 3

the acoustic pressure must be continuous across the boundary. If it were discontinuous then there would be an infinite force as F=-gradp.

Question 4

Continuity of normal particle velocity is what?

Answer 4

The particle velocities normal to the boundaries must be equal. The fluid must stay in contact.

Question 5

What are the pressure transmission and reflection coefficients at normal incidence in the limit that z1» z2?

Answer 5

Z2/Z1=1

R+1=T Therefore T=2

Question 6

How do you relate the intensity reflection and transmission coefficients and for pressure and energy ?

Answer 6

1+R=T

1=Re+Te

Question 7

Scattering

Answer 7

refers to the reflection of sound from surfaces or heterogeneities in a medium. It includes reflection and diffraction

Question 8

Diffraction

Answer 8

is usually used to refer to the ‘leakage’ of sound into ‘shadow zones’. Diffraction is the reason you can hear someone talking in the next room even though you cant see them. The sound waves ‘bend’ around the corners more than light waves do as they have a much longer wavelength.

Question 9

What is the critical angle?

Answer 9

If the incidence angle becomes any larger, then R=1 and the incident wave will be totally reflected.

Question 10

Scattering can be divided into 5 classes

Answer 10

molecular, diffusive, diffractive, specular and moving

Question 11

Describe specular scatter

Answer 11

no wavelength dependence.

wavelength &laquo_space;a. Straightforward reflections as discussed in previous sections.

Question 12

Diffractive scattering

Answer 12

wavelength ~= a includes small cysts or microcalcifications. scatter is anisotropic and there is a variable frequency dependence.

Question 13

Describe diffusive scattering

Answer 13

Small scatterer in which lambda&raquo_space; a for a scatterer with characteristic size a.

Question 14

Name three absorption mechanisms

Answer 14

1) Viscous losses due to shear and compressive stresses
2) Conversion of the wave energy into internal molecular states
3) Thermal conduction between regions of the wave at different temperatures.

basically thermal, and changing the state of the wave(remember they are diff) and a bit o’ friction.

Question 15

If the pressure absorption coefficient alpha = 1dBcm^-1

a) What is the intensity absorption coefficient in dbcm^-1
b) What is the absorption coefficient in Nepers per cm?

Answer 15

a) 2dBcm^-1

b) 2/8.7

Question 16

consistent

Answer 16

if it mathematically reduces to the continuous governing equations in the limit that the spatial and temporal steps reduce to zero.

Question 17

stable

Answer 17

a numerical model is stable if the errors in the numerical solution are bounded, that is they do not grow as the stimulation progresses

Question 18

convergent

Answer 18

a numerical model is convergent if the numerical solution approaches the exact solution as the size of the discrete spatial and temporal steps used in the model is reduced.

Question 19

What is piezoelectricity

Answer 19

a voltage can be generated by applying a compressive or tensile force on the crystal

Question 20

What is pyroelectricity

Answer 20

a voltage can be generated by applying heat as well as a force

Question 21

the piezoelectric materials used in ultrasound transducers have been poled. what is poling and why is this process necessary?

Answer 21

Poling is the process of increasing polarisation of a material by applying an external electric field to align the domains of the material.

Question 22

for a transmitting piezoelectric element with a matched load, show the q factor is 3/4 and the fractional bandwidth is 4/3.

Question 23

transmission constant

Answer 23

strain produced per unit of applied electric field

Question 24

Receiving constant

Answer 24

electric field generated per unit of applied stress

Question 25

electromechanical coupling factor

Answer 25

constant characterising the effectiveness of conversion of electrical energy to mechanical energy and vice versa

Question 26

assuming the sound speed of pzt is 4000m/s what thickness should the piezoelectric element be for a centre frequency of 2MHz?

Answer 26

10^3m

Question 27

What are the steps involved in poling?

Answer 27

1. Heat the material beyond its Curie temperature (⇠200C for PZT).
2. Apply a strong electric field (⇠2 kV/mm) to orientate the dipole moments (the domain
   polarities) in the same direction.
3. Cool the material.
4. Remove the electric field, leaving the polarisations of the domains more-or-less aligned.

Question 28

Two aspects to reducing resonance?

Answer 28

1. Apply a thick absorbing backing, impedance-matched to the element, to absorb the backward travelling waves. This is typically some mixture of epoxy, which is absorbing, and a fillter material, If perfect matching is achieved, ringing is eliminated and the frequency response is the same as the matched load case.
2. Apply a thin layer to the front face of the element with acoustic impedance between that of the element and that of water. This will allow more of the energy to transmit to the tissue and reduce the resonance.

Question 29

What does air-backed mean?

Answer 29

the acoustic properties of the medium adjacent to the rear face of the element are not the same as the element itself. The reflection coefficient for
a wave travelling through the element towards the back face will reflect with a reflection coefficient
of - 1, i.e., it will be inverted.