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# Doppler effect in living tissue

## Problem

Ultrasound is defined as any sound pressure wave which has a frequency above what a human being can hear. Generally speaking, this is any sound above 20kHz. One of the most common uses of ultrasound in medicine is ultrasonic imaging, or sonography. Sonography works by sending ultrasonic waves through the body, and then measuring the reflected waves (or ‘echo’) back from whatever tissues it bounces off. These echoes will reflect differently depending on the attenuation coefficient of the tissue it encounters (table 1), and computers can translate these differences into a visual image. Large attenuation coefficient means that the beam is quickly attenuated (weakened) as it passes through the medium, and a small attenuation coefficient means that the medium is relatively transparent to the beam.
The more consistent the density of medium which the ultrasound waves travel through, the more clear the image will be. Because dry skin contains many pockets of air, a gel is used as a conductive medium that enables a tight bond between the skin and the probe or transducer.
Sonography isn't the only application of ultrasound in medicine however. Like any transmitted wave, ultrasound is also subject to the Doppler effect, meaning that ultrasonic waves can be transmitted through the body in order to determine the speed and direction of moving objects. This is utilized in Doppler echocardiography, which is an imaging technique that measures the speed and direction of blood flow. If blood is flowing in the wrong direction, or at too high or low of a velocity, this can indicate a heart valve defect, as well as a structural abnormalities of the heart which would allow blood to flow improperly to opposite sides of the heart.
Table 1. Attenuation coefficients of sound in various bodily tissues
SubstanceAttenuation coefficient (dB / (MHz x cm))
Air1.64
Blood0.2
Cortical Bone6.9
Brain0.6
Cardiac0.52
Enamel120
Citation: Culjat, Martin O.; Goldenberg, David; Tewari, Priyamvada; Singh, Rahul S. (2010). A Review of Tissue Substitutes for Ultrasound Imaging. Ultrasound in Medicine & Biology 36 (6): 861–873.
Suppose a sonography machine emits a sound wave of 500 kHz into soft tissue. What would the size of the wavelength, given that the speed of sound in soft tissue is 1540 m/s?