1.1 particles move with same wave direction. Fig

1.1 Nature of sound wave:.

Soundwaves is a result of mechanical potential that passes
through medium as a wave gives alternating pressure and rarefaction. And sound
can travel through a liquid , gas and solid, A bell is a common example of
sound that generates vibrations to be heard.

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1.2 Range of sound wave:

Sound which humans can heard start from 20 HZ to 20 KHZ,
while the ultrasound range used  in some
medical application ranges from 2 MHZ to 15 MHZ.

1.3 basic units of measurement for soundwaves.

a- Time period (T): the required time to complete one cycle
(second), T = 1/f.

b-  Frequency (f): is
the number of full cycle in a certain time (HZ), f = 1/T.

c- Wavelength (?): is the distance between trough or crest
of wave (meter).

Fig (1,2)

The figure (1,2) explain the meaning of each parameter in
the wave motion.

1.3a Sound speed equation:

c=f?

C is represent the speed of sound.

1.4 Types of sound propagation.

Transverse wave: wave that the particles is vertical on
direction of wave.

Fig (3)

Longitudinal wave: the particles move with same wave
direction.

Fig (4)

1.5 Acoustic Impedance (Z): is the result of density (?) of
the medium which the sound pass through it and the speed of sound (C).

Z = ?c

And the difference in acoustic impedance determine the
amount of reflection, with large difference acoustic impedance almost of
incident energy will be reflected, while small difference in acoustic impedance
wil reflect apart of incident energy and the remainingwill go forward.( Tissue
properties determine the acoustic impedance).

1.6 Reflection: a sound wave strikes an interface between
two media with perpendicular,  incidence
sound can be reflected . And the amount of reflected sound is expressed as (R)
reflection coefficient.

1.6a Reflection Cases:

a. Specular reflection: have also another name that explain
it more (mirrors for sound), If the interface is large and slick (smooth) and
incident sound energy is approximately in right angle the sound energy will
reflected to source (Transducer) as a mirror reflects light.

b. Diffuse reflection: if the interface is small and rough
it will scatter the the sound energy that falling on it in randomly direction
and only one part will reflect to the sound energy source (Transducer).

Fig (5)

This figure (5) explain the incident sound energy and (A)
expressed specular case (White arrow), While (B) expressed Diffuse case, and in
(A) the yellow arrow Illustrates if the incident sound energy not in right
angle the reflected energy will not come back to sound source.

1.6b Reflection coefficient (R):

If the specular reflected is vertical to incident energy we
can calculate reflected energy by this equation:

R=(Z2?Z1)2/(Z2+Z1)2

Z1 is expressed as a acoustic impedance for first medium.

Z2 is expressed as a acoustic impedance for second medium.

1.7 Refraction: Can defines it if the sound energy go from one
medium in a certain speed and specific direction and pass to another medium and
have a change in speed either lower or higher and the direction will be
different, ratio of changing direction is proportional to velocity of sound
energy, have more explain in Snell law.

1.7a Snell law:

sin?1/sin?2=c1/c2

c1 is sound speed in medium 1.

c2 is sound speed in medium 2.

?1 is incident angle.

?2 is refracted angle.

If sound speed in medium 1 is lower than speed in medium 2
the direction of medium 1 will be smaller than medium 2.

Fig
(6)

The figure (6) explain Snell law ( T1,T2,T3 is the refracted
angle and I is incident angle, 1 and 2 is the sound speed).

1.8 Interference of wave:

is the change of when two waves interact with each other,
and it has two types.

a. Destructive interference:

when the waves are 180o out of phase and that occur a no
wave (removed each other).

Fig (7)

b. Constructive interference:

waves that are in Same phase that occur a single wave but
have a higher amplitude.

Fig (8)

1.9 Transmitter:

In an ultrasound imaging, transmitter control the number of
sound wave pulses that released from transducer (that have a name pulse repetition
frequency “PRF”), PRF which is specify the time between pulses of sound wave
that is important to ensure that each pulse back to the transducer before
release a new pulse. (That the pulse in medical imaging composed of 2 to 4
cycles).

1.10 Transducer:

Transducer is an instrument which can change signal or
energy  from one type or form to another
one, these transducers can change multiple forms of energy such as mechanical,
and electrical energy. And there are many types of transducers such as potentiometer
which converts the change in a length of wire to a resistance for the wire, and
strain gage transducer which converts pressure energy into electrical signal,
and Piezo electric transducer convert mechanical energy to electrical energy
and vice versa, the meaning of piezoelectric is the pressure that occurs due to
electricity, these types of transducers are used for ultrasound imaging.
Piezoelectric transducer (PZT) content: it has a crystals (such as quartz) and
ceramic materials that is the functional component of transducer which is have
a role to release mechanical and electrical energy. Piezoelectric transducer
(PZT) work: electricity occur when the crystals be as a battery and have
positive in one face and negative in reverse face and it connected with each
other for current flow to create the circuit, and for opposite operation the
crystals have a mechanical pressure (vibrating) that resulting from voltage
pass through the reverse faces, the crystals vibrate to generate high frequency
(frequency increases with vibrate increasing). Important of PZT: it has high
frequency response and self generating and it affected from temperature
changing.

Fig (9)

This figure (9) explain the parts of piezoelectric transducer.

when the medium (tissue) have a large thickness the sound
will be attenuated, and also when wave come back from medium (such as tissue)
to transducer it will loss an energy of signal, and this problem it can solve
it by controlling time gain compensation (TGC) that placed in receiver, and TGC
allow to have more brightness and higher resolution for image in deeper parts
of the tissue.

Fig (10)

This figure (10) explain that the gain when it increase it
will have a good resolution and brightness for deeper distance and when it not
used it will be a dark and low resolution for deeper distance.

1.12 Attenuation:

When the sound waves travels intensity, power and amplitude
will decrease as it does. Its Units are dB, decibels. Attenuation has Three
Components which are Absorption, Scattering and Reflection. Attenuation related
to frequency, in low frequency will attenuated slower than high frequency.

1.12a Attenuation coefficient of sound (dB/cm/Hz) eq.

?water   =
ln(Vout/Vin)/x

x represent the
distance from one transducer to the other one (between them), Vin represent the
electrical signal which is transmitted, ?water is the attenuation coefficient
and Vout represent the electrical signal which is received.

1.12b factors affecting attenuation:

The factors that have an effect on attenuation frequency
(when it increase the attenuation will increase and vice versa), the travel
distance and tissue nature

Fig (11)

This figure (11) illustrates the attenuation amount in some
medium.

1.13 Arrays:

Basically array produced by slicing transducer element
(crystal) into a many smaller element and these element put in separate places
to prevent any interference (electrical or acoustic) to have a signal without
any problem. And there are types of transducer arrays.

a. Linear array:

It works by firing groups or individual elements in a
sequence and it the beams will be perpendicular to transducer and parallel to
each other, and It is straight and has a rectangular image shape therefore it
is used for small parts such as blood vessels.

b. Curved array:

Is a linear array but with a convex beams to create large
field of view, it is used for larger parts such as pelvic.

c. Phased Array:

in phased array, the transducer elements produced sector
field of view when the elements firing sequentially and controlling it
electronically , and from these the ultrasound beams will be can to go to any
direction and different depths, these arrays is used for neonatal head
ultrasound.

Fig (12)

The figure (12) explain each type of array ( A is linear, B
is curved, C is phased).

1.14 Properties of ultrasound beam:

The beam of ultrasound travels in a longitudinal wave from
transducer to a specified medium, there are two patterns of beam:

a. Near field (Fresnel zone):

Is a converging beam that have a distance determined by
diameter of transducer and wavelength of transmitted ultrasound wave, and the
shape of beam is formed by transducer curvature, then the pressure amplitude is
quite complex and varies greatly. To calculate the length of near field we have
an equation:

Near field length =
d2 / 4?

d is the diameter of transducer.

? is wavelength of
transmitted wave.

b. Far Field (Fraunhofer zone):

Is a diverging beam, and get a less divergence beam in high
frequency and large transducer diameter, the ultrasound beam diverge when the
distance to transducer increases with pressure amplitude decreases. To get the
value of ultrasound beam divergence angle we use this equation:

sin ? = 1.22 ? / d

Where d is diameter of transducer

? the wavelength.

? is the ultrasound beam divergence angle.

Fig (13)

The figure (13) explain briefly the difference between near
and far field and how get the angle of divergence beam.