Sound Wave Properties
Physical Principles
Education>Expert TTE>Basic Principles>Physical Principles>1

Objectives

At the completion of this chapter the student should be able to:

• Discuss the Physical Properties of Sound Waves
• Discuss the Sound Wave Interaction with Tissues
• Explain Transducers
• Discuss Ultrasound Beams

Sound Waves

Sound waves are mechanical vibrations that induce alternate rarefaction (expansion) and compression of any physical medium through which the sound wave travels .  Sound waves cannot travel through a vacuum. Sound wave travel in a straight line and the medium's molecules move back and forth, or longitudinally. Therefore, sound waves are longitudinal waves. Waves that cause a medium to move perpendicular to the wave are called transverse waves. Sound waves have four physical properties: (Figure 1.1.1)

• Amplitude (loudness)
• Wavelength ( )
• Frequency (f)
• Propagation velocity(vp)  Figure 1.1.1 Sound Wave Properties

 The amplitude (or loudness) is the height of the sound wave and is measured in decibels (dB). As the sound wave increases in amplitude the medium will expand (rarefaction). Conversely, when the sound wave decreases in amplitude the medium will compress. When the medium is compressed by a sound wave an acoustic pressure is produced.  A louder sound will produce a higher acoustic pressure than a softer sound. A decibel is the log of a ratio of acoustic pressure (V) and a reference value (R) multiplied by 20.  R is usually 1 (one).  The decibel formula is shown in Figure 1.2.  In table 1.1 some common examples of sounds and their usual decibel level are shown. dB = 20 * log(V / R) Figure 1.1.2 Decibel Formula
 Decibel Level Example 30 Quiet Library 40 Living Room, refrigerator 50 Light traffic, normal conversation 60 Air conditioner, sewing machine 70 Vacuum cleaner, hair dryer, noisy restaurant 80 Average city traffic, garbage disposal, alarm clock 90 Subway, motorcycle, lawn mower, truck traffic 100 Garbage truck, chain saw 120 Rock band concert, Thunder 140 Gunshot, jet plane 180 Rocket launch Table 1.1.1 Decibel Levels

The wavelength is the length of one wave cycle (i.e. from peak to peak) which includes one rarefaction and one compression and is measured in millimeters (mm).  The propagation velocity is the velocity of the wave thru a medium.  The propagation velocity is dependent upon the medium's characteristics (i.e. density, temperature).  The propagation velocity of average human tissue is 1540 m/sec . In Table 1.2 common propagation velocities are listed for different tissues.
 Tissue Velocity of Sound (m/sec) Air 330 Fat 1450 Water 1480 Average Human   Soft Tissue 1540 Brain 1540 Liver 1550 Kidney 1560 Blood 1570 Muscle 1580 Lens of Eye 1620 Skull Bone 4080 Table 1.1.2 Velocity of Sound in Biologic Tissues

The frequency of a sound wave is the number of cycles of a sound wave per second or  Hertz (Hz). The frequency can be calculated by dividing wavelength by time (Figure 1.3).    A small wavelength will yield a higher frequency, whereas a larger wavelength will yield a smaller frequency.  The human hearing range is 20-20,000 Hz.  Ultrasound is greater than 20,000 Hz.  Medical ultrasound is typically 1-20 MHz, or megahertz .  One megahertz(MHz) is equal to 1 million Hertz.  Figure 1.1.3 Low Frequency Figure 1.1.4 High Frequency

f = cycles / sec Frequency Wavelength (l) 3 MHz 0.5 mm 5 MHz 0.3 mm 7 MHz 0.2 mm
Figure 1.1.5 Frequency Formula Figure 1.1.6 Ultrasound Ranges Table 1.1.3 Wavelengths

Period

A period is the time it takes for a single cycle to occur. From the start of one cycle to the start of the next cycle is called the period. While period is measured in time, wavelength is measured in length. A period is determined by the sound source, not the medium through which the ultrasound signal travels. Period and frequency are inversely related. A high frequency wave has a short period and a low frequency wave has a long period. Figure 1.1.7 Amplitude and Period

Relationship between Wavelength, Frequency, and Propagation

Propagation velocity, c,  is the distance that a sound wave travels in a medium in one second. Propagation velocity is determined by the medium through which the ultrasound wave travels. Sound waves of the same frequency travel at different propagation velocities in different mediums. Sound waves of different frequencies will travel at the same propagation velocity in the same medium.  Figure 1.1.8 Sound Waves in Different Mediums Figure 1.1.9 Sound Waves in Same Medium

Propagation velocity is the product of wavelength (y) and frequency .  If the medium is human soft tissue, then the propagation velocity (c) is 1540 m/sec. The wavelength can be calculated by dividing 1540 m/sec by the frequency.   Note that wavelength is inversely proportional to frequency.  A higher frequency will have a shorter wavelength.
 c = y x f c = 1540 m/sec y = 1540 / f Table 1.1.4 Wavelength-Frequency Relationship

As a sound wave travels from one medium to another medium, the propagation velocity changes. Since the wavelength of a sound wave is determined by the transducer, the frequency changes. The change in frequency is called a frequency shift. Figure 1.1.10 Frequency Shift

Penetration

As the ultrasound beam penetrates a medium, the beam is attenuated or loses energy.  As a beam penetrates tissue, some of the beam is reflected, refracted or absorbed as heat generation. The amount of penetration will determine the depth of the scanning area.  Penetration is directly related to wavelength.  Smaller wavelengths are more easily reflected or refracted in the superficial tissues than longer wavelengths. As wavelength is increased (or frequency decreased) the ultrasound will penetrate deeper.  As the wavelength is decreased (or frequency is increased) the ultrasound beam will have a shallower penetration. Low frequency ultrasound has superior penetration.

Resolution and Penetration Relationship Figure 1.1.11 Resolution-Penetration Chart

Since wavelength and frequency are inversely related, so to, are resolution and penetration inversely related.  The frequency can be adjusted on transesophageal echocardiography machines from 3 MHz to 7 MHz.  In the 3 MHz setting, there will be improved penetration so deep structures can be evaluated.  In the 7 MHz position, the superficial structures can be displayed with improved resolution.  Figure 1.6 depicts the relationship between resolution and penetration.

At the high penetration/low resolution settings the deeper structures are more easily visualized at the loss of resolution of the more superficial structures. At the opposite setting, the high resolution/low penetration setting, the deep structures are not well visualized while the superficial structures are sharp and exhibit enhanced detail.

 High Penetration Low Resolution Mixed Low Penetration High Resolution   Amplitude

Amplitude is equivalent to loudness and is measured by the distance from the baseline to the peak of the ultrasound wave. Measuring from the bottom peak to the top of the peak of the ultrasound wave is a peak-to-peak amplitude and is twice the size of the ultrasound's amplitude.  If the echocardiography machine cannot 'hear' the returned signal (echo) then, if the machine 'yells louder', it may hear the louder echo. Increasing the amplitude increases the acoustic pressure or the pressure generated by the sound waves.  Amplitude is measured in decibels.  A decibel is equal to 20 times the log of the acoustic pressure divided by a reference value (typically 1 (one).  If the amplitude is doubled the decibel level will increase by 6. Table 1.5 and Figure 1.7 show a logarithmic rise in acoustic pressure is proportional to the rise in decibels.  Figure 1.1.12 Amplitude Figure 1.1.13 Acoustic Pressure vs. Decibels

 Acoustic Pressure(V) Formula db=20 * log(V/R) Calculation Decibel (dB) 2 dB = 20 * (log(2/1) dB = 20 * 0.3 6 10 dB = 20 * (log(10/1) dB = 20 * 1 20 100 dB = 20 * (log(100/1) dB = 20 * 2 40 1000 dB = 20 * (log(1000/1) dB = 20 * 3 60 10,000 dB = 20 * (log(10,000/1) dB = 20 * 4 80 100,000 dB = 20 * (log(100,000/1) dB = 20 * 5 100 Table 1.1.5 Acoustic Pressure and Decibel Level

Phase

An ultrasound transducer, when set on a single frequency, can produce a small range frequencies called a bandwidth. Some of the frequencies produced enhance the single frequency wave if the waves are in Phase. Ultrasound waves that are in phase have matching amplitudes and the amplitude of the single frequency wave is enhanced. If the amplitude of the ultrasound wave does not match then interference occurs and the amplitude of the single frequency wave is diminished.  Figure 1.1.14 Sound Waves in Phase -> Enhancement Figure 1.1.15 Bandwidth Results in Areas of Enhancement  Figure 1.1.16 Sound Waves Out of Phase -> Interference Figure 1.1.17 Sound Waves Out of Phase -> Interference

Magnitude

Magnitude describes the strength of an ultrasound wave. Magnitude is determined by:

• Amplitude
• Power
• Intensity

Power is the rate of energy transfer and is measured in watts. As power is increased the amplitude of the wave increases. Light a light bulb, if power is increased the light bulb is brighter. Power is directly proportional to the amplitude squared.

Power ~ Amplitude2

Intensity is the concentration of energy in a sound wave. Intensity is calculated by dividing the ultrasound wave's power by the cross sectional area. Intensity is similar to thickness of the ultrasound wave. If an ultrasound wave has high intensity then the power is either high or the cross sectional area of the wave is small. Intensity is measured in watts/cm2 and is given by the formula:

Intensity (W/cm2) = Power (W) / Area (cm2) This activity has been planned and implemented in accordance with the accreditation requirements and policies of the Accreditation Council for Continuing Medical Education through the joint providership of University of Nebraska Medical Center, Center for Continuing Education and JLS Interactive, LLC.
The University of Nebraska Medical Center, Center for Continuing Education is accredited by the Accreditation Council for Continuing Medical Education to provide continuing medical education for physicians. This activity is approved by the American Society of Radiologic Technologists (ASRT) as sonography-related continuing education (CE). Credit(s) issued for successful completion of ASRT-approved CE activities are accepted by the American Registry of Diagnostic Medical Sonography, American Registry of Radiological Technologists, Cardiovascular Credentialing International and Canadian Association of Registered Diagnostic Ultrasound Professionals. Contact the applicable registry for additional information / restrictions on their acceptance of ASRT CE credit.