Physics, Waves

Mediums for sound waves are _________, _________, or _________.

solid, liquid or gas

Propagation speed

speed at which sound moves through a given medium. Units: m/s or mm/μsec c=fλ

Acoustic Impedance

the acoustic resistance to sound traveling in a medium. It is a property of the medium: -Based on density and propagation speed of the medium Acoustic impedance = density x prop speed Z = pc Units: Rayls

Decibels

A decibel (dB) is a unit used to measure the intensity of sound -Higher the decibel level, the louder the noise -Human threshold of hearing is 0 dB means we cannot hear sound doesn't mean that there is no sound It is a ratio between two values of power -Use logarithms with base 10 to express the sound intensity as a multiple of the threshold of hearing

Mechanical waves

A disturbance (oscillation or vibration) that travels through a medium, transporting energy from one location (its source) to another location without transporting matter. Cannot travel in a vacuum

Harmonics

the set of all possible standing waves within a system

Period (T)

the time it takes to complete one cycle Units: seconds, ms, μsec

(Back) Scattering

AKA diffuse reflection. Wave reflected back at many different directions; this type of reflection occurs when the surface is rough relative to the wavelength. Most interfaces in the body are not large and smooth so this is common. Random redirection of sound beam as it strikes an interface in many directions.

Advantage/Disadvantage of (Back) Scattering

Advantage: reflections at suboptimal angles will still be received by the transducer so data is not lost. Disadvantage: backscatter signals are at a lower strength than specular reflections.

Temperature and sound waves

Air temperature impacts how fast sound travels. Molecules at higher temps have more kinetic energy, thus they vibrate faster. -Therefore, sound waves travel faster in warmer temperatures because they are carried faster.

Refraction

Bending of transmitted sound beam due to the wave hitting a boundary of a different medium. Changes the direction the wave travels because of -Change in speed and wavelength of new medium Only occurs if beam is NOT at a normal incidence (perpendicular to boundary)—therefore the beam strikes the interface at oblique incidence.

Power and Amplitude

Directly related Power is proportional to the wave's amplitude squared. P proportional to A^2

Compression

a point in a medium through which a wave has increased density and pressure. Molecules are squeezed together.

Stiffness and Velocity

Directly related: -speed is lowest in gases (air, lungs) -higher in liquids (water, blood, tissue, fat) -highest in solids (metal, bone)

How are frequency and scattering related?

Directly related; higher frequency sound beam scatters more

Rarefaction

a point in a medium through which the wave has decreased density and pressure. Molecules are stretched apart.

Power and Intensity

Power and intensity are directly related. P is proportional to I which is proportional to A^2

What do sound waves travel the fastest through?

Solids; slower through gases

vibration (periodic motion)

back and forth motion that repeats itself

Pressure

Sound is a traveling pressure variation that transfers energy (not particles) through a medium (matter). P = F/A It starts as normal undistributed value (baseline position), increases to a maximum value (compression), returns to normal, decreases to a minimal value (rarefaction) and returns back to normal.

Ultrasound Propagation speed

c = 1.54 mm/μsec OR 1540 m/s Average speed of sound in soft tissue CANNOT be altered by the sonographer or ultrasound unit. Only changes when the medium through which it travels changes. Determined by density and stiffness of the medium

In ultrasound, increasing the frequency...

decreases penetration and increases image quality (resolution)

Period and Wavelength

directly related (time vs. length)

Attenuation and distance

directly related; attenuation increases as distance (or path length) increases

Speed of a wave

distance traveled (wavelength) by a given point on the wave in a given period of time (period). Speed = Wavelength / Period S = λ ÷ T

Equilibrium position

when an object has not been disturbed; no force applied to the mass

Density

is associated with the pressure variation; direct relationship As sound travels through a medium, its pressure increases and decreases causing variations in density. greater the pressure, higher the density

Absorption

is the conversion of sound energy into other forms of energy, in this case heat within the medium.

Absorption Critical Points

1. Absorption is the main factor creating attenuation in soft tissue. -Absorption accounts for about 80% of a sound beam's attenuation in soft tissue. 2. Absorption increases exponentially with increasing frequency. -Absorption increases as intensity increases 3. Absorption reduces the amount of energy there is to reflect a sound wave echo. -This reduces penetration and signal strength. 4. The energy being absorbed causes tissue heating. -A potential risk of thermal tissue damage, or thermal bioeffects because of the increase in intensity.

3 Types of Reflection

1. Specular Reflection 2. (Back) Scattering 3. Rayleigh Scattering

Categories of Sound

1. Ultrasound (Supersonic) - >20,000 Hz (or >20 kHz) 2. Audible Sound - 20 Hz-20,000 Hz 3. Infrasound (Subsonic) - <20 Hz

3 types of attenuation

1. absorption 2. reflection 3. scattering

The nature of the molecules of the solid, liquid, or gas determines how well or rapidly the substance will carry the sound wave. Depends on...

1. the inertia of the molecules 2. the strength of the interaction

Important Facts about Scattering, Specular Reflections & Rayleigh Scattering

A homogenous medium would produce no echoes (anechoic) since there would be no acoustic impedance mismatch. Fluids tend to be homogenous and consequently anechoic (no echoes). Most surfaces in the body are "rough" with respect to the wavelength of diagnostic ultrasound producing scattering. The scattering gives the apparent tissue texture to ultrasound. Tissues are never truly homogenous therefore producing varying degrees of echogenicity. Tissue is much more specular in nature compared to blood. The best images are produced when the angle of incidence is perpendicular to the surface of the structure. Most specular reflectors in the body are of little interest & most often cause imaging artifacts. Examples of very strong specular reflectors are bones, diaphragm, and gas.

Reverberation

A reflected sound wave arriving in less than 0.1 s after the original sound was sent out. Sounds like an increase in volume because of mixing of reflected sounds with its original sound or prolonged sound.

Important facts

As frequency increases, the wavelength decreases, making the surfaces within the body appear rougher. As a result of increasing the frequency: -the amount of scattering increases and -absorption increases Therefore, -attenuation increases and -decreased penetration results from the less energy being transmitted through the tissue.

Acoustic Variables

Changes due to a mechanical interaction of the sound wave through a medium. Describe the rhythmic changes in time of the sound wave. 1. Pressure 2. Density 3. Distance (particle motion) 4. Temperature

Distance/particle motion

Changes in pressure and density by traveling sound energy causes the particles in the matter to vibrate (oscillate) back and forth. This passes the energy on to the neighboring molecules by causing them to vibrate in the same manner. There is no permanent displacement of the molecule; molecules return to resting state after the energy has been transferred.

Logarithm

Count the number of zeros i.e. 1000 = log 3, .01 = log -2

Frequency and Wavelength

Frequency and wavelength are inversely proportional in a given medium Lower the frequency, the longer the wavelength. Increased penetration but decreased resolution

Diffraction

Happens when a wave hits a sharp obstacle, corner, or gap. Diffraction is the greatest when the gap is about the same size as the wavelength of the wave. The waves bend around the object or spread out when they pass through the gap. The wave changes shape.

Frequency in Ultrasound

In ultrasound, a wave's frequency is the number of cycles that occur in one second. Clinical Imaging frequencies: 1.0-15.0 MHz

Inverse Square Law

Intensity is proportional to 1/distance^2 The farther from the source (increase in distance), the lower the intensity (decrease). Intensity and distance are inversely related

Intensity and Amplitude

Intensity is proportional to the wave's amplitude squared. I is proportional to A^2

Intensity

Is the measure of energy the sound wave is carrying. Intensity = power/area I = P/A Units: watts/meter squared (W/m2) Determined by the source (ultrasound system) and is important when discussing bioeffects. Can be changed by the operator using the power control. This will change the amplitude of the wave.

Reflection

Is the mechanism which makes US work. When a wave front strikes a boundary perpendicular to the wave front, the wave may be absorbed, transmitted or reflected (back to the sound source) or a mixture of some or all of these 3 depending on the boundary medium. -Hard surfaces reflect more -Soft surfaces absorb more Part of the beam is still transmitting through the tissue and is weakened at each interface.

What happens to wave amplitude with propagation through tissue?

It decreases

Continuous sound waves

No image provided; continuously sending

Frequency and speed

Not related! Different quantities

destructive interference

Occurs when both waves intersect "out-of-phase." The peak of one wave lines up with the trough of the other, (the maximum & the minimum amplitudes of both waves occur at different times). This results in a decrease in amplitude or a canceling out of the wave altogether. This contributes to ultrasound attenuation.

Rayleigh Scattering

Occurs when dimensions of an object are much smaller than the wavelength of the beam Most common form: -Red Blood Cells! -Diameter of RBC is << λ Increases dramatically with increase in frequency Rayleigh Scattering is proportional to Frequency^4 More scatter because more reflections - not traveling as deep so hitting more surfaces faster.

Interference

Occurs when two waves overlap at the same location and at the same time. Thus, they combine. The resulting overlap is the formation of a single, new wave that is the sum of the two original waves. Interference of two waves can result in an increase or decrease in amplitudes.

Doppler effect in Ultrasound

Red blood cells are the moving source If the red blood cells are moving towards the transducer, then the transducer will think there is an increase in frequency and thus a positive Doppler shift. If the red blood cells are moving away from the transducer, then the transducer will think there is a decrease in frequency and thus a negative Doppler shift.

Power

Refers to the strength of the sound beam. -It is the amount of work/time. P = W/t Determined by the sound source (ultrasound unit) -Can be changed by the operator by adjusting the power control or output power control Power decreases as ultrasound travels through the body.

Stiffness

Rigidity of an object; hardness; the ability of a material to maintain its shape even when pressure is applied to it. i.e. bone Opposite of flexibility or pliability.

Pulsed sound waves

Send and receive waves that reflect off body structures and provide an anatomical image using the piezoelectric effect.

How fast does sound travel compared to light?

Slow; i.e. light of lightning and the sound of thunder

Doppler

Sounds from moving sources; i.e. sirens, red blood cells

Combine interference

Superposition of non-identical waves exhibits both constructive and destructive interference.

Period and Frequency

T=1/f or f=1/T; Inversely related If period increases, then frequency decreases Use "opposite" units: Mega (10^6) & Micro μ (10^-6) Ex: 4 MHz = ¼ μsec

Doppler effect

The Doppler Effect is produced by a moving source of waves: -There is an apparent upward shift in frequency when the sound wave source approaches you and -There is an apparent downward shift in frequency when the sound wave source moves away from you. Note: The effect does not result because of an actual change in frequency of the source. Occurs for all waves including electromagnetic waves.

Acoustic Impedance (Z) and Gel

The acoustic impedance of air is extremely low. When the US beam strikes the air-tissue interface, almost the entire beam is reflected (99.9%) leaving nothing be transmitted to the second medium for an image. The acoustic impedance of gel is higher than the impedance of air, minimizing this mismatch (reducing the reflection) and allowing for more sound transmission (energy) into the body to generate the image.

The type of reflection that occurs at tissue boundaries impacts...

The amount of energy reflected back to the probe. The strength of the return signal depends on how much of the wave energy is reflected back to & received by the transducer: the stronger the backscatter, the stronger the signal. If too much reflection occurs at one boundary, there will not be enough energy left to visualize deeper tissue boundaries.

Reflection and Transmission

The amount of reflection and transmission from an interface of two mediums is determined by the acoustic impedance mismatch (or differences). % Reflection = (Z2-Z1/Z2+Z1)^2 x 100 When there is a large difference (mismatch) between the acoustic impedances of the two interfacing media, there is a large reflection and a small transmission. % reflected + % transmitted = 100%

Specular Reflection

The angle of incidence equals the angle of reflection; Occurs at large, smooth and flat surfaces relative to the wavelength.

Negative Decibels

The final intensity < the original intensity. The signal is weakened. Below the threshold of hearing. It is a decrease in intensity and amplitude as sound travels through tissue. It is expressed as −dB as the intensity decreases

Positive decibels

The final intensity > original intensity. The signal is strengthened. Above the threshold of hearing. Example: Turning up the gain on the machine = adding decibels = stronger echoes

constructive interference

The interference that occurs when two waves combine to make a wave with a larger amplitude. Occurs when both waves intersect "in-phase" so crests match and troughs match

Frequency

The number of cycles that occur in a specific duration of time. It is a rate! A complete cycle is one crest and one trough. Units: Hertz (Hz) Frequency = v/λ

Loudness Parameters

These parameters illustrate size and strength of a wave: 1. Amplitude 2. Power 3. Intensity 4. Pressure The operator can change these by adjusting power on the ultrasound unit.

Sound waves are mechanical waves because...

They cannot travel through a vacuum. Their molecules vibrate back and forth from a fixed position. They must travel through a medium in which the molecules are alternately compressed and rarefied. They travel in a straight line. They are longitudinal waves.

Why are acoustic qualities needed?

They help the sound wave be heard clearly and cleanly

Pulsed Ultrasound

Two Parts: Transmit (or sending) Time -"talking time"; time it is 'on' Receiving Time -"listening time"; time it is 'off' Unlike continuous waves, pulsed waves have a small break between wave cycles in order to "listen" for beam that is returning.Imaging systems produce short bursts (or pulses) of energy to create anatomical pictures. Pulse = Train Both are made up of individual compartments but both move as a whole down the 'track.' Pulse has individual cycles but together moves as a whole through the body and back to the transducer.

Piezoelectric Effect

Ultrasound transducers have a piezoelectric material in them. Converts electrical energy to mechanical energy (sound waves) then converts the mechanical energy back to electrical energy. The most notable piezoelectric material is quartz. There are also manufactured materials with the most commonly chosen one being lead zirconate titanate (PZT).

How does a sound beam interact with a medium?

When an incident sound wave (original intensity) encounters an interface: 1. Reflection 2. Absorption 3. Transmission As a sound wave meets an interface between 2 media: -part of it is reflected back to the transducer (weakening the wave's intensity), -part of it is absorbed into the tissues, -and the rest propagates through the interface.

Dispersion

When waves with different wavelengths creating different propagation speeds cause the waves to spread out.

Echo

a reflected sound that can be distinguished from the original sound because of a time delay -Ultrasound echoes are waves reflected off of tissue and make an image on the screen. A reflected sound wave that arrives more than 0.10 s after the original sound was sent out. -The human ear can distinguish the reflected sound from the original sound when it's been longer than 0.10 s.

Medium

a substance or material that carries the wave

Longitudinal wave

a wave in which particles of the medium move in a direction parallel to the direction that the wave moves. Longitudinal waves are always characterized by particle motion being parallel to wave motion.

Transverse wave

a wave in which particles of the medium move in a direction perpendicular to the direction that the wave moves. Transverse waves are characterized by particle motion being perpendicular to wave motion.

Doppler Shift Equation

doppler shift = reflected frequency - transmitted frequency

In ultrasound, decreasing the frequency...

increases penetration and decreases image quality (resolution)

Attenuation in Ultrasound

is the decrease in intensity & amplitude of a sound wave as it travels through a medium and is absorbed. It is the weakening or reduction of the wave due to the interaction with the medium. The body absorbs the ultrasound energy making the waves disappear. These waves don't "return" to the transducer. The more body tissues the wave has to cross the more the attenuation the wave suffers.

Amplitude

is the strength of a sound wave. It is the maximum displacement of the particles of the wave. i.e. the peak pressure, strength, or loudness. depends on the 4 acoustic variables

Wavelength

length of one complete wave cycle; repeating pattern Units: mm or meters

Attenuation (continued)

makes ultrasound work or not work is measured in decibels (-dB: the intensity is weakening & therefore decreasing. The negative sign is assumed when referring to attenuation). affects the image quality (must be compensated for through the components & controls of the US unit) Without understanding attenuation effects, it is impossible to understand how & why the US system controls work.

Sound waves are _________, _________ waves

mechanical and longitudinal

Sound waves require a ____ to travel through.

medium

Antinodes

places of constructive interference

Nodes

places of destructive interference

fundamental frequency

the longest wave possible in a standing wave with one antinode and 1/2 wavelength determines the pitch of the basic musical note and is called the first harmonic

Amplitude (A)

the maximum amount of displacement of a particle through the medium from its equilibrium related to the amount of energy carried by a wave

What happens as the amount of force in a sound wave increases?

the pressure increases, area decreases, and the sound gets louder

Simple harmonic motion

the vibratory motion that occurs when there is a restoring net force opposite to and proportional to the displacement. -Periodic vibration (or oscillation) of the mass. -A spring will continue to vibrate back and forth until it reaches a state of equilibrium where the force is zero.

Attenuation

the weakening of the sound beam as it passes through tissue.

pure constructive interference

two identical waves produce one with twice the amplitude, but the same wavelength

pure destructive interference

two identical waves produce zero amplitude, or complete cancellation.

Wave equation

v=fλ

Standing waves

waves that just vibrate up and down in place; need a medium that is fixed or bounded. i.e. guitar string, a lake, air in a room Two waves with the same amplitude, wavelength and frequency that are traveling in opposite directions. Interferences makes them appear to not move.

Resonance

when the frequency of an external force matches the natural frequency of an object. Energy is transferred very efficiently i.e. when a singer breaks a water glass by matching the resonant (or natural) frequency of the glass