Doppler ultrasound is based on the shift of frequency in an ultrasound wave caused by a moving reflector, such as blood cells in the vasculature. Suppose that a stationary transducer (both speaker and microphone) directs ultrasounds of frequency 5 MHz toward a wall of blood cells ("Roll Tide!") moving toward the transducer with a speed of 0.50 m/s. The speed of sound in blood is assumed to be similar to water Vsound = 1500 m/s. I) Treat the blood moving toward the source as a moving observer (with positive velocity) and apply the Doppler shift equation to find the frequency of the ultrasound observed by the moving blood wall. (see Eq. 16-8 and keep lots of sig. figs.!) Hz foi = fal ¹+ 1
Doppler ultrasound is based on the shift of frequency in an ultrasound wave caused by a moving reflector, such as blood cells in the vasculature. Suppose that a stationary transducer (both speaker and microphone) directs ultrasounds of frequency 5 MHz toward a wall of blood cells ("Roll Tide!") moving toward the transducer with a speed of 0.50 m/s. The speed of sound in blood is assumed to be similar to water Vsound = 1500 m/s. I) Treat the blood moving toward the source as a moving observer (with positive velocity) and apply the Doppler shift equation to find the frequency of the ultrasound observed by the moving blood wall. (see Eq. 16-8 and keep lots of sig. figs.!) Hz foi = fal ¹+ 1
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![## Doppler Echocardiography - Double Doppler Shift:
Doppler ultrasound is based on the shift of frequency in an ultrasound wave caused by a moving reflector, such as blood cells in the vasculature.
Suppose that a stationary transducer (both speaker and microphone) directs ultrasound of frequency 5 MHz toward a wall of blood cells ("Roll Tide!") moving toward the transducer with a speed of 0.50 m/s. The speed of sound in blood is assumed to be similar to water: \( v_{\text{sound}} = 1500 \, \text{m/s} \).
### I) Calculations
1. **Treat the blood moving toward the source as a moving observer (with positive velocity) and apply the Doppler shift equation to find the frequency of the ultrasound observed by the moving blood wall.**
(see Eq. 16-8 and keep lots of sig. figs!)
\[
f_{o1} = f_{s1} \left( \frac{1 + \frac{v_o}{v_s}}{1} \right) = \_\_\_\_\_\_ \, \text{Hz}
\]
### II) Reflection and Emission
2. **Treat the blood as a source of reflected sound, emitting frequency \( f_{s11} = f_{o1} \) moving toward the transducer - now the observer (microphone). Calculate the frequency heard in the reflection.**
(Keep lots of sig. figs.)
\[
f_{o11} = f_{s11} \left( \frac{1}{1 - \frac{v_s}{\_\_}} \right) = \_\_\_\_\_\_ \, \text{Hz}
\]
### III) Beat Frequency
3. Though the ultrasound frequencies (5 MHz) are far above the audible range, the Doppler frequency shifts for moving blood occur in the audible range. It is both customary and convenient to convert these frequency shifts into an audible signal through a loudspeaker that can be heard by the sonographer to aid in positioning and to assist in diagnosis.
4. **Calculate the beat frequency between the frequency emitted by the transducer (initial source) and the Double-Doppler-boosted reflected frequency detected by the transducer (final observer).**
\[
f_{\text{beat}} = f_{o11](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e8eea05-bfa1-4cf3-87d5-3720d24ea670%2Fa2c14cd5-80eb-4f69-a52e-81bfccb57b56%2Fyi9ppbm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Doppler Echocardiography - Double Doppler Shift:
Doppler ultrasound is based on the shift of frequency in an ultrasound wave caused by a moving reflector, such as blood cells in the vasculature.
Suppose that a stationary transducer (both speaker and microphone) directs ultrasound of frequency 5 MHz toward a wall of blood cells ("Roll Tide!") moving toward the transducer with a speed of 0.50 m/s. The speed of sound in blood is assumed to be similar to water: \( v_{\text{sound}} = 1500 \, \text{m/s} \).
### I) Calculations
1. **Treat the blood moving toward the source as a moving observer (with positive velocity) and apply the Doppler shift equation to find the frequency of the ultrasound observed by the moving blood wall.**
(see Eq. 16-8 and keep lots of sig. figs!)
\[
f_{o1} = f_{s1} \left( \frac{1 + \frac{v_o}{v_s}}{1} \right) = \_\_\_\_\_\_ \, \text{Hz}
\]
### II) Reflection and Emission
2. **Treat the blood as a source of reflected sound, emitting frequency \( f_{s11} = f_{o1} \) moving toward the transducer - now the observer (microphone). Calculate the frequency heard in the reflection.**
(Keep lots of sig. figs.)
\[
f_{o11} = f_{s11} \left( \frac{1}{1 - \frac{v_s}{\_\_}} \right) = \_\_\_\_\_\_ \, \text{Hz}
\]
### III) Beat Frequency
3. Though the ultrasound frequencies (5 MHz) are far above the audible range, the Doppler frequency shifts for moving blood occur in the audible range. It is both customary and convenient to convert these frequency shifts into an audible signal through a loudspeaker that can be heard by the sonographer to aid in positioning and to assist in diagnosis.
4. **Calculate the beat frequency between the frequency emitted by the transducer (initial source) and the Double-Doppler-boosted reflected frequency detected by the transducer (final observer).**
\[
f_{\text{beat}} = f_{o11
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