[Ultrasound Physics] SOUND WAVES

[Contents]

1. Acoustic Waves (= Sound waves)

2. Mechanical Waves

3. Terms Describing Sound Waves/The Properties of Sound

4. Terms describing Pulsed Waves

5. Levels of Sound

1. Acoustic Waves

 

1) Traveling variation (oscillation) in acoustic variables

- Molecules oscillate back and forth to propagate sound waves

- Do not move from one end of the medium to another

- Acoustic variables

: Temperature

: Pressure - Concentration of force in an area

: Density - Concentration of mass in a volume

: Distance - Measure of particle motion

2) Mechanical longitudinal wave

 

3) Vacuum: a space void of matter

- Sound cannot travel in a vacuum

- Electromagnetic radiation, light/x-ray can travel through a vacuum

2. Mechanical Waves

 

1) require a medium for propagation (gas, liquid, or solid)

- cause motion of the particles they are moving through

- molecules do not travel from one end to the other (it is not a flow of particles). 

: Molecules vibrate back and forth

- can be either Transverse or longitudinal.

 

2) Longitudinal Waves

- particles of medium vibrating in the same direction as the wave propagation direction

- sound: mechanical longitudinal wave

 

3) Transverse Waves/Shear Waves/Stress Waves

- propagates by particles of the medium moving perpendicular to the wave propagation direction.

- Bone: The only biological tissue that can cause the production of transverse waves 

3. Terms Describing Sound Waves/The Properties of Sound [★★]

1) Compression (Compression zone, Peak, Up-hump, Wavefront, Leading portion of a wave)

- High pressure region of the wave form

- Area of maximum particle density

 

2) Rarefaction (Trough)

- Low pressure region of the wave form

- Area of minimum particle density

 

3) Cycle

- one high pressure and one low pressure region of a wave.

 

4) Frequency (f)

- The number of cycles that occur in one second [MHz, kHz or Hz]

: F = 1/p (frequency = 1/period)

: F= c/λ (frequency = propagating speed/wavelength)

- Hertz (Hz): One cycle per second

: MHz = 1,000,000 cycles/second  

: kHz = 1,000 cycles/sec

- Diagnostic ultrasound frequency Range: 1-16MHz

- frequency is important in diagnostic ultrasound: affects penetration and image quality.

 

5) Period (T)

- Time it takes for one cycle to complete itself [seconds(s) or microseconds (μs)]

- Time between two successive compression zones or rarefaction zones

: T = 1/f (Period = 1/frequency)

: frequency and period are reciprocals

 

6) Wavelength (λ)

-

- The distance one cycle takes up [meters(m), centimeter (cm), or millimeter (mm)]

-  The distance between two successive density zones.

: λ = c/f (wavelength = Propagating speed/frequency)

- wavelength and frequency: inversely proportional

 

7) Propagation

- Changes in pressure conveyed from one location to another                          

 

8) Propagating Speed (Acoustic Velocity)

- speed of sound moving through a medium. [mm/us or m/s]

- c = f (Hz) x λ (m)

- Determined only by the medium. Especially, the density and stiffness of the medium

: Stiffness - the ability of a material to resist compression

- Stiffness has a greater effect on PS than density

- Stiffness and Propagating Speed: proportional

: ↑ Stiffness = ↑ PS

: Density - relative weight of the material

- Density and propagating speed: inversely proportional

: ↑ Density = ↓ PS

 : Not operator adjustable

- Materials that are very stiff but not dense will have the highest propagating speed.

- Materials that are not very stiff but are extremely dense will have the lowest propagating speed.

- Propagating speed in soft tissue: 1.54mm/us or 1540 m/s

- speed used to calibrate range-measuring circuits on diagnostic sonography instruments: 1540 m/s

- Tissue Type & Correlating Speeds

: Propagating speed through gas is low

: Propagating speed through liquid is higher 

: Propagating speed through a solid is the highest.              

- Air: 300 m/s

- Lung: 500 m/s

- Fat: 1,450 m/s

- Water: 1,480 m/s

- Soft Tissue.: 1,540 m/s

- Liver: 1,560 m/s

- Blood: 1,560 m/s

- Muscle: 1,600 m/s

- Tendon: 1,700 m/s

- Bone: 3,500 m/s ~ 4080 m/s

- Metals: 2,000 – 7,000 m/s

 

9) Properties of the medium that effect Propagating Speed

- Elasticity

: the ability of an object to return to its original shape and volume after a force

: Force applied to an object cause a change in its shape or volume (distortion)

- The strength of the force determines the amount of distortion.

- Density (d)

: The mass of a medium per unit volume. 

               : The relative weight of an object.

: d = m/v

- larger mass requires more force to cause motion

- larger mass requires more force to stop molecules already in motion

- Density and propagating speed: inversely proportional

- Stiffness (s, = Bulk Modulus)

: an objects ability to resist compression

: the inverse of compressibility

              : Stiffness and Propagating Speed: proportional

- Compressibility (K)

: The fractional decrease in volume when pressure is applied to the material

: stiffness ↑→ compressibility ↓, acoustic velocity ↑

 

10) The source is able to determine the Period (T), Frequency (f), Amplitude, Power, and Intensity

- The source does not determine the Propagating Speed(c) (the medium does)

- Frequency is not related to propagating speed (propagating speed is a constant in soft tissue)

- Wavelength is determined by both the medium and the source

 

11) Interference [★★]

- algebraic summation of waves leading to patterns of minima and maxima

- interference patterns of reflected waves cause acoustic speckle

               : to reduce speckle

                              - use frame averaging (persistence)

                              - use compound imaging

- two waves overlap at the same location, at the same time

               : combine into a single new wave

- constructive interference: sound waves are in phase and resulting amplitude is increased

- destructive interference: amplitude of new wave is decreased

               : complete destructive interference creates black pixels

4. Terms describing Pulsed Waves [★★★]

 

1) Pulse “A Burst of Cycles”

- collection/group of two or more cycles followed by a resting time.

- We use pulsed waves for diagnostic ultrasound

- pulsed wave US is necessary for real-time imaging

               : depth of interface from which the echo originated can be determined

 

2) Pulse Duration (PD)

- Time from the beginning to the end of a single pulse of ultrasound

- Time it takes for one pulse to occur (excludes the resting time) [μs]

: PD = n x T (Pulse Duration = number of cycles x Period)

- not operator adjustable

 

3) Pulse Repetition Period (PRP)

- The amount of time from the start of one pulse to the start of the next pulse

: includes resting time, sound on and off time [μs]

: PRP = 1/PRF

- operator adjustable, determined by sound source

- unrelated to period

 

4) Pulse Repetition frequency (PRF)

- The number of pulses that an ultrasound system transmits into the body each second [MHz or Hz]

               : rate at which the transmitter applies electronic voltage pulses to the transducer

: PRF = 1/PRP

- Along with PRP, determine the maximum imaging depth (depth of view)

- Determined by

: Sound source (pulser)

: operator adjustable

: Determined by the maximum imaging of the system

- limited by the speed of sound in tissue

               : there must be enough time between pulses for US to travel to and back from the reflector

               : or else, range ambiguity occurs

               : if sound travels faster in tissue, maximum PRF can be increased

- Relationships

: PRF & depth of view – inversely proportional

               - imaging depth ↓ → short listening time, PRP ↓, PRF ↑

- Imaging depth ↑ → longer listening time, PRP ↑, PRF ↓

: PRF & PRP – inversely proportional

: PRF and frame rate - proportional

                              - PRF ↑ → frame rate ↑

- If PRF is too high for the imaging depth: range ambiguity

               : a pulse should be received before the next pulse is transmitted

               : if pulse is transmitted before echoes from first pulse are received

                              → echoes would be misplaced axially on the image

- operator adjustable.

- pulsed-wave doppler: PRF ↑ → acoustic exposure ↑

 

5) Spatial Pulse Length (SPL)

- the length of space over which one pulse occurs [mm]

: SPL = n x λ (Spatial pulse length = number of cycles x wavelength)

: frequency ↑ → wavelength ↓, SPL ↓

- shorter pulses → better images

- pulse duration ↓ → SPL ↓ → better axial resolution

 

6) Duty Factor (DF)

- The fraction of time the transducer is actively transmitting sound

- It compares on and off time.

: DF = PD/PRP

: PRP ↑ → DF ↓.

: PRP ↓ (PRF ↑) → DF ↑

- for sonographic systems: averages between 0.2% - 0.5% (0.1% - 1%)

5. Levels of Sound

-

1) Infrasound

- a frequency of less than 20Hz.

- A sound frequency too low for human hearing

 

2) Audible Sound

- The range of human hearing: 20-20,000Hz

 

3) Ultrasound

- 20,000Hz or higher (high frequency mechanical waves that humans cannot hear)

- A sound frequency too high for human hearing

 

Reference

 

* Davies Ultrasound Physics review

* https://sites.google.com/site/lindadmsportfolio/ultrasound-physics/

* https://sites.google.com/site/nataljasultrasoundphysics/

* https://sites.google.com/site/ektasphysicseportfolio/doppler