Chapter 3 SPI Physics: Describing Sound Waves

Acoustic Parameters

describe the wave’s features

• Frequency

• Period

• Amplitude

• Power

• Intensity

• Wavelength

• Propagation Speed

acoustic = ___ parameter = ____

sound, characteristic

Period (def, units, values, determined, adjustable)

time required to complete a single cycle or time form start of one cycle to start of the next

UNITS: time - seconds, milliseconds, hours, days

VALUES: 0.06-0.5 microseconds

DETERMINED: by sound source ONLY

ADJUSTABLE?: No, once transducer is selected

Frequency (f) (def, units, values, determined, adjustable)

number of particular events in a specific duration of time (CYCLES PER SECOND IN ULTRASOUND)

• how often an event occurs per time

  • once per day

  • once per century

  • 3 times per minute

UNITS: per second (known as hertz or Hz)

• one cycle/second = 1 Hz

VALUES: 2MHz - 15MHz per second

DETERMINED: by sound source ONLY

ADJUSTABLE?: No, once transducer is selected

• increased frequency = less penetration through the body

Frequency of a sound wave refers to

how many compressions or rarefaction cycles that occur per time (usually per second)

• one compression per cycle = 1 Hz

For each compression, there is a rarefaction.

How do we Determine the Frequency?

• determined by the sound source

• count the number of compression per second

• MORE compressions per second = HIGHER frequency

Infrasonic

below threshold of human hearing

• less than 20 Hz

Audible

in range of human hearing

• between 20 Hz and 20 kHz

Ultrasound

above threshold of human hearing

• greater than 20 kHz

Relationship Between Frequency and Period

• inversely related

  • when one goes up, the other goes down

• Hertz (per second) is the inverse of time

• As frequency increases, period decreases

• As frequency decreases, period increases

• If one remains constant, the other does not change

• Period * frequency = 1 (reciprocals)

“Bigness” Parameters

Amplitude

Power

Intensity

• describe a sound beams strength

• directly related to each other

  • as one increases, the others increase

  • as one decreases, the others decrease

Amplitude (def, units, values, determined, adjustable)

“bigness” of a wave, measured from baseline to max value (or min value)

• maximum variation of an acoustic variable

• technically defined as strength, volume, or size of a physical quantity

UNITS: any acoustic variable

• pressure (pascals)

• density (g/cm³)

• distance (cm, ft, etc)

• temperature (degrees, celsius)

VALUES: 1 million pascals to 3 million pascals (1MPa-3MPa) in clinical imaging

DETERMINED: by sound source initially, then the medium

ADJUSTABLE?: Yes, initial amplitude is adjustable

Info about Amplitude

• determined by the sound source as it depends on the voltage applied to the transducer

• higher voltage = high amplitude

• if you turn the volume up on the radio, you make it louder meaning you increase the amplitude, or make the amplitude higher

• amplitude decreases as sound propagates through the body (attenuates)

• unit of measure depends on the acoustic variable being measured

• adjusted by output power

• if you increase the amplitude of an ultrasound echo, the image will get brighter

Peak to Peak Amplitude

can measure difference from max to min and divide in half

How to calculate Amplitude

1. MAX - MEAN

2. MEAN - MIN

3. (MAX - MIN)/2

Power (def, units, values, determined, adjustable)

rate of energy transfer, or rate that work is performed. Also describes “bigness”

• rate of energy transfer in the cross section of the ultrasound beam

UNITS: Watts (W) or milliwatts (mW) (think lightbulb)

VALUES: 0.004 to 0.090 watts, or 4 to 90 milliwatts

DETERMINED: by sound source initially, then the medium as sound propagates through the body power decreases— the extent is dependent on sound wave AND medium

ADJUSTABLE: Yes, initial power is adjustable

Amplitude and Power Relationship

• directly proportional

• Power ⍺ amplitude²

• power controls the amplitude of the wave

• if amplitude is increased by a factor of 3, power has increased by 9

• if sonographer cuts the amplitude in half —> (1/2)²=1/4

• higher power = stronger ultrasound beam = better penetration BUT at the cost in creased risk of bioeffects

Intensity (def, units, values, determined, adjustable)

concentration of energy in a sound beam, also describe “bigness”

• beam power/ beam’s cross-sectional area = intensity

UNITS: watts/cm² (watts from power, cm² from beam area)

VALUES: 0.01 to 300 W/cm²

DETERMINED: by sound source INITIALLY, then the medium as sound propagates through the body intensity changes — this depends on the medium and SHAPE of sound beam

HIGH POWER over a small area = GREAT INTENSITY BUTTT increases the risk of bioeffects

Power, Intensity, & Amplitude Relationships

• intensity ⍺ power

• power ⍺ amplitude²

SO

• intensity ⍺ amplitude²

increasing intensity by decreasing the area (narrowing sound beam) and focusing it on a certain point

Wavelength (λ) (def, units, values, determined, adjustable)

• distance or length of one complete cycle

• measure from one point on the wave to the NEXT IDENTICAL point

UNITS: meters, millimeters, unit of length

VALUES: specifically in soft tissue: 0.1 to 0.8 mm

DETERMINED: by BOTH the SOURCE and the MEDIUM

ADJUSTABLE: No, once transducer has been selected

Wavelength and Frequency Relationship

• inversely related

• frequency increases, wavelength decreases

• RULE: 1.54/Frequency = Wavelength

• shorter wavelengths produce better image quality (THINK HIGHER FREQUENCY)

Wavelength Equation

Wavelength (λ) = propagation speed (c)/ frequency (𝑓)

OR

Wavelength (λ) × frequency (𝑓 )= propagation speed (c)

Propagation Speed (or propagation velocity) (def, units, values, determined, adjustable)

• distance a sound wave travels through a medium in 1 second

• answers how long it will take to get from one location to another

• UNITS: meters/second, mm/millisecond, or any distance divided by time

• VALUES: 500 m/s - 4000 m/s depending on tissue

• DETERMINED: by MEDIUM ONLY

  • speed is determined by the density and stiffness of the medium

  • Every frequency travels the same speed in a particular medium

• ADJUSTABLE?: No, only a change in medium changes the speed

Speed

• apply to ultrasound, the average speed in soft tissue is:

  • 1.54 mm/μs

  • 1540 m/s (one mile per second)

WHY IS THIS IMPORTANT?:

• By knowing the speed in soft tissue, the ultrasound machine can calculate the go return time and then calculate the distance of each structure, then knowing where to place it on the image.

• Distance= rate (speed) x time (machine knows how long the echo took to

return)

Speed in Mediums

• Different mediums have different speeds

  • Stiffness and Density affect speed

  • Sound travels fastest in solids

  • Medium speed in liquids

  • Slowest in gases

EXAMPLES:

• Very stiff + NOT dense = fast speed (bone)

• Not stiff + very dense= Slow speed (air)

Speed Formulas

Propagation Speed = stiffness/density

Propagation Speed = frequency x wavelength

Stiffness

• ability of an object to resist compression

  • “squishability”

• directly related to speed (and has the greatest impact on speed)

Bulk Modulus Definition

• describes the change in materials volume under external stress

• same as stiffness

• change in pressure divided by the fractional change in volume

• basically, how much does the volume of an object shrink down under pressure change

Bulk Modulus Continued

• stiffer material = larger bulk modulus

• more elastic materials = smaller bulk modulus

• c = Bulk modulus/density

• Propagation velocity is impacted more by BM stiffness compared to density

• Therefore, stiffness plays a greater role

• Examples:

• Bone is very dense but also very stiff, therefore it has increased

propagation velocity due to stiffness, rather than decreased due to its

density

• The marshmallow that is very compressible will have a smaller/lower bulk modulus than the rock that cannot compress easily

Density

• mass per volume: density (𝜌) = m/v

• larger mass within the same volume increases density

• two objects of similar volume can have very different densities

• density and speed are inversely related

Rule of Thumbs

• bone is NOT compressible and has tight molecular bonds so speed is fastest

  • bone is stiff but not dense

• gas is very compressible and contains freely moving wide spaced molecules, so speed of sound is slowest in gas or air

  • gas is dense and not stiff

Frequency in terms of speed

Acoustic waves with different frequencies travel at the same speed through the same medium

What is the Speed of Sound in:

Lung

Fat

Soft Tissue (average)

Liver

Blood

Muscle

Tendon

Bone

memorize