Ultrasound, which consists of sound waves with frequencies...

Ultrasound, which consists of sound waves with frequencies above the human audible range, can be used to produce an image of the interior of a human body. Moreover, ultrasound can be used to measure the speed of the blood in the body; it does so by comparing the frequency of the ultrasound sent into the body with the frequency of the ultrasound reflected back to the body's surface by the blood. As the blood pulses, this detected frequency varies. Suppose that an ultrasound image of the arm of a patient shows an artery that is angled at $\theta=20^{\circ}$ to the ultrasound's line of travel (Fig. $17-47 ) .$ Suppose also that the frequency of the ultrasound reflected by the blood in the artery is increased by a maximum of 5495 Hz from the original ultrasound frequency of $5.000,000 \mathrm{MHz}$ . (a) In Fig. $17-47$ , is the direction of the blood flow rightward or leftward? (b) The speed of sound in the human arm is 1540 $\mathrm{m} / \mathrm{s}$ . What is the maximum speed of the blood? (Hint: The Doppler effect is caused by the component of the blood's velocity along the ultrasound's direction of travel.) (c) If angle $\theta$ were greater, would the reflected frequency be greater or less?

Ultrasound, which consists of sound waves with frequencies
above the human audible range, can
be used to produce an image of the
interior of a human body. Moreover,
ultrasound can be used to measure
the speed of the blood in the body; it does so by comparing the frequency of the ultrasound sent into the
body with the frequency of the ultrasound reflected back to the
body's surface by the blood. As the blood pulses, this detected frequency varies. Suppose that an ultrasound image of the arm of a patient shows an artery that is angled at $\theta=20^{\circ}$ to the ultrasound's line of travel
(Fig. $17-47 ) .$ Suppose also that the frequency of the ultrasound
reflected by the blood in the artery is increased by a maximum of 5495 Hz from the original ultrasound frequency of $5.000,000 \mathrm{MHz}$ .
(a) In Fig. $17-47$ , is the direction of the blood flow rightward or
leftward? (b) The speed of sound in the human arm is 1540 $\mathrm{m} / \mathrm{s}$ . What is the maximum speed of the blood? (Hint: The Doppler effect
is caused by the component of the blood's velocity along the ultrasound's direction of travel.) (c) If angle $\theta$ were greater, would the reflected frequency be greater or less?

Key Concepts

Vector Component of Velocity and Angular Dependence

In Doppler ultrasound applications, the measured frequency shift is influenced by the component of the blood's velocity that is in the direction of the ultrasound beam. This dependency is expressed mathematically using the cosine of the angle between the flow direction and the ultrasound beam, meaning that as the angle increases, the effective component (and therefore the observed frequency shift) decreases.

Speed Calculation from Frequency Shift

The relationship between the frequency shift observed in the reflected ultrasound waves and the speed of the blood flow is determined by the Doppler equation. By knowing the original frequency, the measured frequency shift, the speed of sound in the medium, and the beam-tissue angle, one can calculate the maximum speed of the blood.

Ultrasound Imaging

Ultrasound imaging uses high-frequency sound waves, which are above the audible range, to produce images of internal body structures. The technique is based on the reflection and scattering of sound waves by tissues, and its non-invasive nature makes it valuable in medical diagnostics.

Doppler Effect

The Doppler effect refers to the change in frequency or wavelength of waves in relation to an observer who is moving relative to the wave source. In medical ultrasound, it is used to measure blood flow by comparing the frequency of the transmitted ultrasound waves with the frequency of the waves reflected back from moving blood cells.

Transcript

00:01 Between the direction of blood stream and the sound wave.

00:13 The angle is theta and the sound wave is reflecting from, is reflected from the blood cell, from a blood cell.

00:37 And it is observed frequency, see positive frequency shift which had the maximum value of and we can consider a doppler effect and you can consider that this blood cell from which the sound way was reflecting where reflected is moving towards or away towards a source away from the source with the velocity of cosine cosine theta.

01:41 So we consider the projection of this velocity.

01:45 So we have a situation that we have a source of sound waves and something is moving towards this sound waves with the velocity of.

02:07 Or it might move, it might be we get away.

02:13 But which one is possible, which one is correct? and because we have frequency shift is positive, this means that obviously blood cell and frequency, blood cell moves to the right towards the frequency.

02:39 So the answer to the first question would be and what is the velocity? so we would consider this picture so sound waves with the original frequency of f node are reflected from the burlac cell which has a velocity of this and let's imagine hypothetical there is something that could measure the frequency of the sound on the blood cell.

03:41 On the blood cell, what frequency would be measured? f1.

03:48 By the doppler shift, the detector is moving towards the wave.

03:59 This means that frequency should increase.

04:02 So we have v plus speed of the detector over v...

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