What frequency does the blood receive? What frequency return

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SUMMARY

The discussion focuses on calculating the frequency received by blood moving at 28.7 cm/s when mixed with an original frequency of 2.41 MHz. Using the speed of sound in human tissue at 1540 m/s, the observed frequency received by the blood is calculated as 2.410449 MHz. The frequency returning to the source is determined to be 2.410948 MHz, resulting in a beat frequency of 948 Hz when the two frequencies are mixed. The participant initially struggled with parts b and c but later resolved the issues independently.

PREREQUISITES
  • Understanding of the Doppler effect in sound waves
  • Familiarity with frequency calculations and conversions
  • Knowledge of the speed of sound in various media, specifically human tissue
  • Proficiency in using significant figures in scientific calculations
NEXT STEPS
  • Study the Doppler effect in detail, focusing on its applications in medical ultrasound
  • Learn how to perform frequency calculations using the Doppler shift formula
  • Explore the concept of beat frequency and its relevance in wave interference
  • Review OpenStaxCollege Physics, particularly Example 17.8 for practical applications
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Students in physics, medical professionals utilizing ultrasound technology, and anyone interested in the principles of wave behavior and frequency analysis.

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Homework Statement


Ultrasound reflected from an oncoming bloodstream that is moving at 28.7 cm/s is mixed with the original frequency of 2.41 MHz to produce beats. Use the speed of sound in human tissue as 1540 m/s. Assume that the frequency of 2.41 MHz is accurate to seven significant figures. (Hint: compare to Example 17.8 in OpenStaxCollege Physics.)

a) What frequency does the blood receive? (Give an answer in MHz, to 7 significant figures.)

b) What frequency returns to the source? (Give an answer in MHz, to 7 significant figures.)

c) What beat frequency is produced if the source and returning frequencies are mixed? (Give an answer in Hz, to 3 significant figures.)

Homework Equations



f(observed) = f(s) x (Vw / Vw +/- Vs)

f(observed) = f(s) x (Vw +/- V(obs)) / Vw

The Attempt at a Solution



a)
(2,410,000 Hz)(1540 m/s + .287 m/s) / 1540 m/s) = 2410449.136 Hz = 2.410449 MHz

b)
(2410449 Hz)(1540 / 1540 - .287) = 2410948.313 Hz = 2.410948 MHz

c) 2410948.313 - 2410000 = 948 Hza) is correct, I got that one right. b) and c) are wrong. I thought I did them correctly. Could someone please help?
Thank you!
 
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