Resident Physics Lectures 02: Sound Properties and Parameters.

Resident Physics LecturesResident Physics Lectures

02:02:Sound Properties and Sound Properties and ParametersParameters

Sound Wave Definition?Sound Wave Definition?

• Sound is a WaveWave• WaveWave is a propagating (traveling)

variation in a “wave variablewave variable”

• “An elephant is big, gray, and looks like an elephant.”

Sound Wave VariableSound Wave Variable

• Examples– pressure (force / area)– density (mass / volume)– temperature

• Also called acoustic variableacoustic variable

Sound is a propagating (moving) variation in a “wave variablewave variable”

Sound Wave VariationSound Wave Variation

• Freeze time• Measure some acoustic variable as

a function of position

Position

AcousticVariableValue

PressureDensityTemperature

MOREMORE• Make many measurements of an

acoustic variable an instant apart• Results would look the same but

appear to move in space

1

2

MOREMORE• Track acoustic

variable at one position over time

Sound WavesSound Waves• Waves transmit energy• Waves do not transmit matter• “Crowd wave” at sports event

– people’s elevation varies with time– variation in elevation moves around stadium

» people do not move around stadium

Transverse WavesTransverse Waves

• Particle moves perpendicular to wave travel

• Water ripple– surface height varies with time– peak height moves outward

» water does not move outward

Compression (Longitudinal) Waves

Compression (Longitudinal) Waves

• Particle motion parallel to direction of wave travel

1

2

1

2

Wave Travel

Motion ofIndividual Coil

Sound Waves are Compression Waves

Sound Waves are Compression Waves

• Regions of alternating low and high pressure move through air

• Particles oscillate back & forth parallel to direction of sound travel

• Particles do not move length of sound wave

Wave Travel Motion of IndividualAir Molecule

MediumMedium

• Material through which wave moves

• Medium not required for all wave types

– no medium required for electromagnetic waves» radio

» x-rays

» infrared

» ultraviolet

– medium is required for sound» sound does not travel through vacuum

Talk louder! I can’t hear

you.

Sound WavesSound Waves

• Information may be encoded in wave energy

– radio– TV– ultrasound– audible sound

Sound FrequencySound Frequency

• light frequency corresponds to color

• sound frequency corresponds to pitch

Sound FrequencySound Frequency# of complete variations (cycles) of an

acoustic variable per unit time

• Unitscycles per second

1 HzHz = 1 cycle per second

1 kHzkHz = 1000 cycles per second

1 MHzMHz = 1,000,000 cycles per second

• Human hearing range 20 - 20,000 Hz

Sound FrequencySound Frequency

• Ultrasound definition> 20,000 Hz

– not audible to humans» dog whistles are in this range

• Clinical ultrasound frequency range

1 - 10 MHz

1,000,000 - 10,000,000 Hz

PeriodPeriod

• time between a given point in one cycle & the same point in the next cycle

– time of single cycle

• Units– time per cycle (sometimes expressed

only as time; cycle implied)

period

Magnitude of acoustic

variable

time

PeriodPeriod

• as frequency increases, period decreases

• if frequency in Hz, period in seconds/cycle

1Period = ------------------- Frequency

PeriodPeriod

• if frequency in kHz, period in msec/cycle• if frequency in MHz, period in sec/cycle

1 kHz frequency ==> 1 msec period

1 MHz frequency ==> 1 sec period

Period = 1 / Frequency

Reciprocal UnitsReciprocal Units

Frequency Units

Period Units

Hz (cycles/sec) seconds/cycle

kHz (thousands of cycles/sec)

msec/cycle

MHz (millions of cycles/sec)

sec/cycle

Period / FrequencyPeriod / Frequency

If frequency = 2 MHz then sound period is 1/2 = 0.5 sec

If frequency = 10 kHz then sound period is 1/10 = 0.1 msec

If frequency = 50 Hz then sound period is 1/50 = 0.02 sec

If sound period = 0.2 sec then frequency = 1/0.2 = 5 MHz

If sound period = 0.4 msec then frequency = 1/0.4 = 2.5 kHz

If sound period = 0.1 sec then frequency = 1/0.1 = 10 Hz

Sound Period & Frequency are

determined only by the sound source. They are independent of medium.

Who am I?

Burt Mustin

Propagation SpeedPropagation Speed

• Speed only a function of medium

• Speed virtually constant with respect to frequency over clincial range

WavelengthWavelength• distance in space over which single cycle

occurs OR

• distance between a given point in a cycle & corresponding point in next cycle

• imagine freezing time, measuring between corresponding points in space between adjacent cycles

Wavelength UnitsWavelength Units

• length per cycle– sometimes just length; cycle implied

• usually in millimeters or fractions of a millimeter for clinical ultrasound

Wavelength EquationWavelength Equation

Speed = Wavelength X Frequency [ c = X (dist./time) (dist./cycle) (cycles/time)

• As frequency increases, wavelength decreases

– because speed is constant

WavelengthWavelengthSpeed = Wavelength X Frequency

[ c = X (dist./time) (dist./cycle) (cycles/time)

mm/sec mm/cycle MHz

Calculate Wavelength for 5 MHz sound in soft tissue

Wavelength = 1.54 mm/sec / 5 MHz

Wavelength = 1.54 / 5 = 0.31 mm / cycle

5 MHz = 5,000,000 cycles / sec = 5 cycles / sec

Wavelength is a function of both the

sound source and the medium!

Who am I?

John Fiedler

Pulsed SoundPulsed Sound• For imaging ultrasound, sound is

– Not continuous

– Pulsed on & off

• OnOn Cycle (speak)– Transducer produces short duration sound

• OffOff Cycle (listen)– Transducer receives echoes

– Very long duration

ON OFF ON OFF

(not to scale)

Pulse CyclePulse Cycle

• Consists of– short sound transmission

– long silence period or dead time» echoes received during silence

• same transducer used for– transmitting sound– receiving echoes

sound silence sound

Pulsed Sound ExamplePulsed Sound Example

• ringing telephone– ringing tone switched

on & off

– Phone rings with a particular pitch

» sound frequency

sound silence sound

Parameters Parameters

• frequency

• period

• wavelength

• propagation speed

• pulse repetition frequency

• pulse repetition period

• pulse duration• duty factor• spatial pulse

length• cycles per pulse

Sound Pulse

Pulse Repetition FrequencyPulse Repetition Frequency

• # of sound pulses per unit time

• # of times ultrasound beam turned on & off per unit time

– independent of sound frequency

• determined by source

• clinical range (typical values)– 1 - 10 KHz

Pulse Repetition PeriodPulse Repetition Period

• time from beginning of one pulse until beginning of next

• time between corresponding points of adjacent pulses

Pulse Repetition Period

Pulse Repetition PeriodPulse Repetition Period

• Pulse repetition period is reciprocal of pulse repetition frequency

– as pulse repetition frequency increases, pulse repetition period decreases

• units– time per pulse cycle (sometimes simplified to just time)

• pulse repetition period & frequency determined by source

PRF = 1 / PRP

Higher FrequencySame PulseRepetition Frequency

Pulsed SoundPulsed Sound

• Pulse repetition frequency & period independent sound frequency & period

Same FrequencyHigher PulseRepetition Frequency

Pulse DurationPulse Duration• Length of time for each sound pulse• one pulse cyclepulse cycle =

– one sound pulse and one period of silence

• Pulse duration independent of duration of silence

Pulse Duration

Pulse DurationPulse Duration

• units– time per pulse (time/pulse)

• equationpulse duration = Period X # cycles per pulse

(time/pulse) (cycles/pulse) (time/cycle)

Pulse Duration Period

Pulse DurationPulse Duration

Longer Pulse Duration

Shorter Pulse Duration

Same frequency; pulse repetition frequency,period, & pulse repetition period

Pulse DurationPulse Duration

Pulse duration is a controlled by

the sound source, whatever

that means.

Duty FactorDuty Factor• Fraction of time sound generated• Determined by source• Units

– none (unitless)

• EquationsDuty Factor = Pulse Duration / Pulse Repetition Period

Duty Factor = Pulse Duration X Pulse Repetition Freq.

Pulse Duration

Pulse Repetition Period

Spatial Pulse LengthSpatial Pulse Length

• distance in space traveled by ultrasound during one pulse

HEYH.......E.......Y

Spatial Pulse Length

Spatial Pulse LengthSpatial Pulse Length

So, can you like show me an example?

Spatial Pulse LengthSpatial Pulse Length

• depends on source & medium

• as wavelength increases, spatial pulse length increases

Spat. Pulse Length = # cycles per pulse X wavelength

(dist. / pulse) (cycles / pulse) (dist. / cycle)

Spatial Pulse LengthSpatial Pulse Length

• as # cycles per pulse increases, spatial pulse length increases

• as frequency increases, wavelength decreases & spatial pulse length decreases

– speed stays constant

Spat. Pulse Length = # cycles per pulse X wavelength

Wavelength = Speed / Frequency

Why is Spatial Pulse Length Important

Why is Spatial Pulse Length Important

Spat. Pulse Length = # cycles per pulse X wavelength

Wavelength = Speed / Frequency

Spatial pulse length determines axial resolution

Acoustic ImpedanceAcoustic Impedance• Definition

Acoustic Impedance = Density X Prop. Speed

(rayls) (kg/m3) (m/sec)

• increases with higher– Density

– Stiffness

– propagation speed

• independent of frequency

Why is Acoustic Impedance Important?

Why is Acoustic Impedance Important?

• DefinitionAcoustic Impedance = Density X Prop. Speed

(rayls) (kg/m3) (m/sec)

• Differences in acoustic impedance determine fraction of intensity echoed at an interface