Explain the main principles behind the use of ultrasound to obtain diagnostic information about internal body structures.
Data for the acoustic impedances and absorption (attenuation) coefficients of muscle and bone are given in the table below.
The intensity reflection coefficient is given by the expression
The attenuation of ultrasound in muscle follows a similar relation to the attenuation of X-rays in matter. A parallel beam of ultrasound of intensity 
enters the surface of a layer of muscle of thickness 
as shown in the figure below.
The ultrasound is reflected at a muscle-bone boundary and returns to the surface of the muscle. Calculate
the intensity reflection coefficient at the muscle-bone boundary,
the fraction of the incident intensity that is transmitted from the surface of the muscle to the surface of the bone,
the intensity, in terms of , that is received back at the surface of the muscle.
are used in medical diagnosis. Suggest one advantage of the use of high-frequency ultrasound rather than lower-frequency ultrasound.
of a medium.
and 
. The intensity reflection coefficient 
for the boundary between the two media is given by
for fat and for muscle are shown in the table below.
of the layer of fat on an animal, as illustrated in the figure below, is to be investigated using ultrasound.
. The beam is reflected from the boundary between fat and muscle. The intensity of the reflected ultrasound detected at the surface S of the fat is 
. Calculate
is incident normally on a muscle of thickness 
, as shown in the figure below.
. Some data for bone and muscle are given in the table below.
for two media having specific acoustic impedances 
and 
is given by
.
and 
, as illustrated in the figure below.
are used in medical diagnosis. State and explain one advantage of the use of high-frequency ultrasound compared with lower-frequency ultrasound.
. A parallel beam of ultrasound is passed through a muscle of thickness 
.
of some media are given in the table below.
. Determine the wavelength, in 
, of ultrasound of frequency 
in the bone.
is incident normally on the boundary between two media of specific acoustic impedances 
and 
, as shown in the figure below.
.
is given by the expression
is given by the expression
and 
in this expression.
as it enters a muscle. The beam passes through a thickness of 
of muscle before being incident on the boundary with a bone, as shown in the figure below.
.
.
. The total thickness of bone is also 
. The transmitted intensity of the X‑ray beam is 
of the incident intensity. Determine 
.
as it enters a muscle of thickness 
, as illustrated in the figure below.
. The ratio 
is found to be 2.9. Calculate the linear attenuation (absorption) coefficient 
of the ultrasound in the layer of muscle.
varies with time 
according to
. The frequency of the ultrasound generated by the probe is 
. Determine the values of
of some media are given in the table below.
and 
. The intensity reflection coefficient 
for the boundary of these two media is given by:
is incident on the boundary between two media A and B, as illustrated in the figure below.
and 
respectively. The intensity of the beam transmitted through the boundary is 
.
of medium B is 
. Calculate the thickness of medium B required to reduce the intensity of the ultrasound beam to 
of its initial intensity in medium B.
and 
. The magnitudes of the acoustic impedances may be almost equal or very different. State how these differences affect the intensity reflection coefficient at the boundary between the two media.
and 
. State how the ratio
is reduced to 
on passing through a thickness of 
of the medium. Calculate the linear attenuation coefficient 
of the ultrasound beam in the medium.
, as shown in the figure below.
is the intensity just after entering the surface of the fat layer, 
is the intensity incident on the fat-muscle boundary, 
is the intensity reflected from the fat-muscle boundary, and 
is the intensity received back. Some data for the fat are given in the table below.
.
of intensity 
.
