Resident Physics Lectures 02: Sound Properties and Parameters

Sound Wave Definition? Sound is a Wave Wave is a propagating (traveling) variation in a “wave variable” “An elephant is big, gray, and looks like an elephant.”

Sound Wave Variable Examples Also called acoustic variable pressure (force / area) density (mass / volume) temperature Also called acoustic variable Sound is a propagating (moving) variation in a “wave variable”

Sound Wave Variation Freeze time Measure some acoustic variable as a function of position Pressure Density Temperature Acoustic Variable Value Position

MORE Make many measurements of an acoustic variable an instant apart Results would look the same but appear to move in space 1 Instant #1 Instant #2 2

MORE Track acoustic variable at one position over time

Sound 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 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 Particle motion parallel to direction of wave travel 1 1 Motion of Individual Coil 2 2 Wave Travel

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 Individual Air Molecule

Talk louder! I can’t hear you. Medium 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 Waves Information may be encoded in wave energy radio TV ultrasound audible sound

Sound Frequency light frequency corresponds to color sound frequency corresponds to pitch

Sound Frequency # of complete variations (cycles) of an acoustic variable per unit time Units cycles per second 1 Hz = 1 cycle per second 1 kHz = 1000 cycles per second 1 MHz = 1,000,000 cycles per second Human hearing range 20 - 20,000 Hz

Sound 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

Magnitude of acoustic variable Period 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) Magnitude of acoustic variable period time

Period = ------------------- Frequency 1 Period = ------------------- Frequency as frequency increases, period decreases if frequency in Hz, period in seconds/cycle

Period = 1 / Frequency Period if frequency in kHz, period in msec/cycle if frequency in MHz, period in msec/cycle 1 kHz frequency ==> 1 msec period 1 MHz frequency ==> 1 msec period

Reciprocal Units Frequency Units Period Units Hz (cycles/sec) seconds/cycle kHz (thousands of cycles/sec) msec/cycle MHz (millions of cycles/sec)

Period / Frequency If frequency = 2 MHz then sound period is 1/2 = 0.5 msec 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 msec 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 Sound Period & Frequency are determined only by the sound source. They are independent of medium. Who am I? Burt Mustin

Propagation Speed Speed only a function of medium Speed virtually constant with respect to frequency over clincial range

Wavelength 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 Units length per cycle sometimes just length; cycle implied usually in millimeters or fractions of a millimeter for clinical ultrasound

Wavelength Equation Speed = Wavelength X Frequency [ c = l X n ] (dist./time) (dist./cycle) (cycles/time) As frequency increases, wavelength decreases because speed is constant

Wavelength Speed = Wavelength X Frequency [ c = l X n ] (dist./time) (dist./cycle) (cycles/time) mm/msec mm/cycle MHz Calculate Wavelength for 5 MHz sound in soft tissue Wavelength = 1.54 mm/msec / 5 MHz 5 MHz = 5,000,000 cycles / sec = 5 cycles / msec Wavelength = 1.54 / 5 = 0.31 mm / cycle

Wavelength is a function of both the sound source and the medium! Who am I? John Fiedler

Pulsed Sound For imaging ultrasound, sound is On Cycle (speak) Not continuous Pulsed on & off On Cycle (speak) Transducer produces short duration sound Off Cycle (listen) Transducer receives echoes Very long duration ON OFF ON OFF (not to scale)

Pulse Cycle Consists of same transducer used for short sound transmission long silence period or dead time echoes received during silence same transducer used for transmitting sound receiving echoes sound sound silence

Pulsed Sound Example ringing telephone ringing tone switched on & off Phone rings with a particular pitch sound frequency sound sound silence

Parameters pulse repetition frequency frequency period Sound Pulse pulse repetition frequency pulse repetition period pulse duration duty factor spatial pulse length cycles per pulse frequency period wavelength propagation speed

Pulse 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 Period time from beginning of one pulse until beginning of next time between corresponding points of adjacent pulses Pulse Repetition Period

Pulse 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

Pulsed Sound Pulse repetition frequency & period independent sound frequency & period Same Frequency Higher Pulse Repetition Frequency Higher Frequency Same Pulse Repetition Frequency

Pulse Duration Length of time for each sound pulse one pulse cycle = one sound pulse and one period of silence Pulse duration independent of duration of silence Pulse Duration

Pulse Duration units equation time per pulse (time/pulse) pulse duration = Period X # cycles per pulse (time/pulse) (cycles/pulse) (time/cycle) Pulse Duration Period

Pulse Duration Longer Pulse Duration Same frequency; pulse repetition frequency, period, & pulse repetition period Shorter Pulse Duration

Pulse Duration Pulse duration is a controlled by the sound source, whatever that means.

Duty Factor Fraction of time sound generated Determined by source Units none (unitless) Equations Duty Factor = Pulse Duration / Pulse Repetition Period Duty Factor = Pulse Duration X Pulse Repetition Freq. Pulse Duration Pulse Repetition Period

Spatial Pulse Length distance in space traveled by ultrasound during one pulse H.......E.......Y HEY Spatial Pulse Length

So, can you like show me an example? Spatial Pulse Length So, can you like show me an example?

Spat. Pulse Length = # cycles per pulse X wavelength Spatial Pulse Length Equation Spat. Pulse Length = # cycles per pulse X wavelength (dist. / pulse) (cycles / pulse) (dist. / cycle) depends on source & medium as wavelength increases, spatial pulse length increases

Spat. Pulse Length = # cycles per pulse X wavelength Spatial Pulse Length Spat. Pulse Length = # cycles per pulse X wavelength Wavelength = Speed / Frequency as # cycles per pulse increases, spatial pulse length increases as frequency increases, wavelength decreases & spatial pulse length decreases speed stays constant

Why is Spatial Pulse Length Important Spat. Pulse Length = # cycles per pulse X wavelength Wavelength = Speed / Frequency Spatial pulse length determines axial resolution

Acoustic Impedance Definition increases with higher 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? Definition Acoustic Impedance = Density X Prop. Speed (rayls) (kg/m3) (m/sec) Differences in acoustic impedance determine fraction of intensity echoed at an interface