2. Resident Physics Lectures 02: Sound Properties and Parameters

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

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

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

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

7. MORE Track acoustic variable at one position over time

8. 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

9. Transverse Waves Particle moves perpendicular to wave travel Water ripple –surface height varies with time –peak height moves outward »water does not move outward

10. Compression (Longitudinal) Waves Particle motion parallel to direction of wave travel 1 2 1 2 Wave Travel Motion of Individual Coil

11. 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

12. 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.

13. Sound Waves Information may be encoded in wave energy –radio –TV –ultrasound –audible sound

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

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

16. 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

17. 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) period Magnitude of acoustic variable time

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

19. Period 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

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

21. Period / 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

22. Sound Period & Frequency are determined only by the sound source. They are independent of medium. Who am I? Burt Mustin

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

24. 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

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

26. Wavelength Equation Speed = Wavelength X Frequency [ c = X  (dist./time) (dist./cycle) (cycles/time) As frequency increases, wavelength decreases –because speed is constant

27. Wavelength Speed = 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

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

29. Pulsed 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 ONOFFONOFF (not to scale)

30. Pulse 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

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

32. Parameters frequency period wavelength propagation speed pulse repetition frequency pulse repetition period pulse duration duty factor spatial pulse length cycles per pulse SoundPulse

33. 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

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

35. 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

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

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

38. units –time per pulse (time/pulse) equation pulse duration = Period X # cycles per pulse (time/pulse) (cycles/pulse) (time/cycle) Pulse DurationPeriod

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

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

41. 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

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

43. So, can you like show me an example?

44. Spatial 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)

45. Spatial 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

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

47. Acoustic Impedance Definition Acoustic Impedance = Density X Prop. Speed (rayls) (kg/m 3 ) (m/sec) increases with higher –Density –Stiffness –propagation speed independent of frequency

48. Why is Acoustic Impedance Important? Definition Acoustic Impedance = Density X Prop. Speed (rayls) (kg/m 3 ) (m/sec) Differences in acoustic impedance determine fraction of intensity echoed at an interface