Ultrasound Physics Chapter 3 Describing Sound Waves

Chapter 3: Describing Sound Waves • Acoustic Parameters describe the features of a sound wave. • There are 7 parameters that we use to completely characterize a wave. • You must know • the units for each parameter • understand how the parameters are related to one another • Whether or not we can change the parameter Sound source vs. Medium • If you know whether a parameter is determined by the sound source or the medium, you can understand how the parameter relates to ultrasound physics. The sound source • The ultrasound system and transducer. • The quantity or level of some parameters is established by the ultrasound system. • Some of these levels can be changed by turning a knob on the machine, others cannot. The medium • The medium or material through which the sound travels • In the case of diagnostic medical sonography, the medium is soft tissue. • The speed of sound in soft tissue is 1540 m/s. • This can also be expressed as 1.54 mm/µs and 1.54 km/s • It is important to understand whether you have the ability to change the value of a parameter while using a single transducer. • We should also know the typical values of a parameter as it applies to diagnostic medical sonography. Describing Sound Waves • Acoustic variables • inform us which waves are sound waves • Acoustic parameters • describe the features of a sound wave 3 Acoustic Variables • Acoustic variables identify certain waves as sound waves-when an acoustic variable changes in time, a sound wave is present • Pressure- concentration of force within an area (Pascals) • Density-concentration of mass within a volume (kg/cm cubed) • Distance-measure of particle motion (units of distance: feet, cm, miles) Describing sound waves • Just as you may describe yourself as 5 feet, 5 inches tall, 150 lbs etc. you must also describe similar features of a sound wave. Parameters that describe sound waves • Period • Frequency • Amplitude • Power • Intensity • Speed • Wavelength Period • The time required to complete a single cycle • can also be described as the time from the start of a cycle to the start of the next cycle Period • Example: the cycle of the earth circling the sun is 365 days • Units of time • Typical values for ultrasound 0.1-.05 microseconds • Determined by the sound source • Can it be changed by the sonographerno Period Period Which strip below has a longer period for each cycle? Frequency • The number of events that occur in a duration of time • Example: what is the frequency of your birthday? • In ultrasound, frequency is the number of cycles that occur in one second Frequency • Measured in hertz (cycles/second) • Determined by the sound source • Cannot be changed by the sonographer • Frequency affects penetration and image quality Frequency One Cycle Cycle 1 – Cycle 2 - 1 second Frequency The frequency of sound determines whether it is ultrasound, audible sound or infrasound • Ultrasound-frequency exceeds 20,000 Hz or 20 kHz • Audible sound is between 20 Hz and 20,000 Hz • Infrasound is less that 20 Hz and is not audible Physics: Describing Sound Waves Frequency Frequency Typical Ultrasound Values 2 MHz to 10Mhz What is the frequency of each strip if the time is 1 sec? What is the frequency of each strip if the time is 2 sec? What is the frequency of each strip if the time is 0.5 sec? The relationship between Frequency and Period • Period and frequency have an inversere relationship. • More specifically, they are reciprocals • As frequency increases, period will decrease proportionally • As period increase, frequency will decrease proportionally • If period does not change, frequency does not change Remember Reciprocals • What • What • What • What • What is is is is is the the the the the reciprocal reciprocal reciprocal reciprocal reciprocal of of of of of ½? 0.5? 2? 3? 0.25? • Since frequency and period are reciprocals what happens to each parameter in these situations? • If frequency is doubled, period is ____. • If period is doubled, frequency is ____. • If period is tripled, frequency is ____. • If frequency is quartered, period is ____. Frequency Frequency x period = 1 • Remember: • If a wave takes longer to complete, we must have fewer waves per second. • If a wave completes a cycle more quickly, we will have more waves completed in each second. Which frequency is highest (each take place in 1 second)? A B C D Which frequency is lowest (each take place in 1 second)? A B C D FREQUENCY (f) Formula: Frequency (MHz) = propagation speed (mm/µs) wavelength (mm) In soft tissue, what is the frequency of a wavelength measuring 1 mm? FREQUENCY • ANSWER: 1.54 MHz The “Bigness” Parameters • Tell us how big or how strong a wave is • Amplitude • Power • Intensity The “Bigness” Parameters: Amplitude • Amplitude – the difference between the average value and the maximum or minimum value of an acoustic variable • The “bigness” or height of a wave Amplitude • Units are those of the acoustic variables (pressure - Pascals, density - cubic cm, particle motion) • Typical values: 1MPa to 3 MPa (MegaPascals) • Determined by sound source • CAN be changed by the sonographer • Amplitude decreases as sound propagates through the body Amplitude Displacement from the average Amplitude Amplitude Displacement from the average Peak to peak amplitude – the difference between the minimum amplitude and the maximum amplitude. Peak to peak amplitude The “Bigness” Parameters – Power • Power-the rate of energy transfer • Units are watts (W) • Determined by the sound source • Typical values: 0.004 – 0.09 watts (490milliwatts) • Power decreases as sound propagates through the body Power • Power is proportional to the amplitude of the wave squared • Power  amplitude2 • With this equation: we will always calculate power when given an amplitude. Example A sonographer increases the amplitude of a wave by a factor of 3. How has the power changed? Remember our equation: Power  amplitude2 Simply plug in the change in amplitude. In this case it was increased by a factor of 3. Power  32 32 =3x3 SO Power would increase by 9! Example Example: The sonographer decreases the amplitude by ½. What is the change in power? Remember our equation: Power  amplitude2 Simply plug in the change in amplitude. Power  1/22 •½x½=¼ • Power is ¼ of what it was. Your turn! • Example: The sonographer decreases the amplitude by 1/5. What is the change in power? • The sonographer doubles the amplitude. What is the change in power? The “Bigness” Parameters - Intensity • Intensity - the concentration of energy in a sound beam • Describes the bigness of a wave • Relates to how the power in a beam is distributed in space. • Intensity depends on the amount of power in a beam and the area of which the power is applied. Intensity • Intensity(watts/cm2) • Watts = power • cm2 = beam area • Intensity = power(watts)÷beam area (cm2) • Determined by sound source • Can be changed by the sonographer (since power can be changed so can intensity) • Typical ultrasound values- 0.001100watts/cm2 INTENSITY Sunlight does not normally ignite a fire When sunlight is focused, intensity increases, and ignition can occur How is intensity related to power and amplitude? • Intensity is proportional to power • So…if power is doubled, intensity is doubled • If power is quartered, intensity is quartered If power proportional to intensity, what do we know about the relationship between intensity and amplitude? The reasoning behind it: • If power  amplitude2 And… • Power  intensity then… • Intensity  amplitude2 Other Intensity related math Often you will be asked how intensity changes when another variable changes. Example: Power is doubled and beam area remains unchanged. How will intensity change? Solve it: • Power is doubled and beam area remains unchanged. How will intensity change? • First, you will use the equation for intensity: • Next, plug in the changes to the equation. • Doubled = 2 • Unchanged = 1 • Halved = ½ • So…. • Intensity = and therefore intensity is doubled Lets try another: • The power of a wave is doubled. If intensity remains the same, what must happen to beam area? • Intensity = power/beam area • In this case intensity =1, power =2 and beam area is unknown… • 1= • Beam area x 1 =2 • Beam area = 2, so the beam area is doubled! Your Turn • Power of a wave is quadrupled. The intensity is halved. What must happen to beam area? Wavelength • The length or distance of a single complete cycle. Wavelength • Units: meters or any unity of length • Determined by sound source and medium through which it travels • Cannot be changed by the sonographer • Typical ultrasound values-0.1-0.8 mm (in soft tissue) • Wavelength is the ONLY parameter determined by the source and medium Wavelength Wavelength - Which strip has cycles with the longer wavelength? Wavelength Wavelength is the only parameter determined by the source and the medium! The relationship between wavelength and frequency • Wavelength and frequency are inversely related. • As wavelength increases, frequency decreases. • As wavelength decreases, frequency increases. • Higher frequency = shorter wavelength • Lower frequency = longer wavelength The wavelength equation: propagation speed mm/ms l = __________________________ frequency (MHz) ( l is the symbol for wavelength, remember it because it looks like a wave!) Use your triangle trick here too! • When using the wavelength equation we have to make sure our units match the units in the equation. • Wavelength should be in mm • Propagation speed should be in mm/ms • Frequency should be in MHz • If you are given a value that is not in this format you have to convert! • Ex: if frequency is in Hertz you have to convert to megahertz! Physics: Describing Sound Waves  Wavelength & Frequency  Inversely related (as long as the wave remains in one medium) As frequency increases, wavelength decreases. Ex: If a wave’s frequency is twice that of another, the wavelength will be half. Physics: Describing Sound Waves Wavelength in Soft Tissue  In soft tissue, sound with a frequency of 1MHz has a wavelength of 1.54 mm.  Relationship between frequency & sound in soft tissue: Divide 1.54mm by the frequency in MHz.  wavelength = 1.54 mm/µs frequency (MHz) Shorter wavelength sound = higher resolution WAVELENGTH (L) Formula: Wavelength (mm/µs) (mm) = Propagation speed Frequency (MHz) WAVELENGTH • What is the wavelength of a 10MHz transducer traveling through soft tissue? • λ= • = 0.154 mm • With a constant propagation speed • If wavelength increases, frequency decreases (inversely proportional). REFER TO PAGE 41 FOR EXAMPLES OF FREQUENCY AND WAVELENGTH • What is the wavelength of a sound wave with a frequency of 2 MHz in soft tissue? •l= • = 0.77 • l = 0.77 mm Important! • In order to use 1.54 mm/ms as your speed of sound you must be informed that the medium is soft tissue!! • If you are not provided with a speed of sound, and it is not indicated that your medium is soft tissue, you do not have enough information to solve the problem. • If you are provided with a speed of sound, and frequency, simply ‘plug’ it into the equation. Why do we care about wavelength? • Wavelength is important in image quality. • Shorter wavelength sound produces higher quality images with greater detail. • This is why high frequency transducers provide better resolution because high frequency is associated with shorter wavelength. Propagation Speed • The rate that sound travels through a medium • The distance that sound travels in 1 second Calculating propagation speed (2 ways) • If you are given frequency and wavelength you can calculate propagation speed by using the wavelength equation • You may also be asked to calculate propagation speed using distance traveled and time that it took. • Example: A sound wave travels 10 cm in 2 seconds. What is the propagation speed in this medium? • Divide the distance by the time • 10cm/2sec = 5 cm/sec (the units carry over!) Speed • Units: meters per second or mm/ms • Determined by: medium only • All sound will travel through any given medium at the same speed regardless of frequency or any other parameter value. Equation for Propagation Speed Propagation Speed = frequency x wavelength Why? Wavelength is determined by the sound source and the medium. By knowing wavelength, and initial frequency of the sound, we can calculate propagation speed! What is interesting about this equation? it is the same equation that is used to calculate wavelength! It is Just arranged in a different way. Properties of Medium and Speed • Speed of sound is related to stiffness and density of a medium • Stiffness • a medium’s ability to be moved • Density • related to a medium’s weight • how closely packed the molecules in that medium are • Stiffness and Speed-directly related • Density and Speed-indirectly related • Stiffness has more of an impact on speed than density • Bulk modulus is the same as stiffness General Rules • Sound travels the fastest in a medium that is low density and high stiffness • Sound travels slowest in a medium that is very dense and not very stiff. Speed of sound in various types of tissues/media • Gas has the slowest speed of sound, liquid is in the middle, and solids have the fastest speed of sound. • General rule: gas< liquid< solid • Hint: think about the stiffness or resistance to pressure of these media! Sound and Soft Tissue • The speed of sound in soft tissue is 1540 m/s. • This can also be reported as • 1.54 km/s • 1.54 mm/ms • 1540 m/s is approximately 1 mile/second Important Sound Speeds • • • • • • Air- 330 m/s Lung – 300-1200 m/s Fat – 1450 m/s Soft tissue – 1540 m/s Tendon- 1850 m/s Bone 2000-4000 m/s • KNOW THESE! Speed of sound in soft tissue General rule: Slowest Fastest • KNOW THIS TOO! Acoustic Parameters  Period  Frequency  Amplitude  Power  Intensity Reciprocals Can be Changed by Sonographer Speed Determined by Sound Wavelengt h Determined by Medium Determined by Both sound source and medium