Doppler Effect with heart motion

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SUMMARY

The discussion centers on calculating the Doppler Effect related to a heart's ventricular wall moving in simple harmonic motion. The heart wall has an amplitude of 1.8 mm and a frequency of 115 beats per minute. A motion detector emits sound at 2,000,000 Hz, traveling through tissue at 1.50 km/s. The maximum linear speed of the heart wall is determined to be 1.5 m/s, and the calculations for the maximum frequency of sound arriving at the heart and received by the motion detector are discussed, emphasizing the need to apply the Doppler Effect formula accurately.

PREREQUISITES
  • Understanding of simple harmonic motion
  • Familiarity with the Doppler Effect formula: f' = f0((Vo + Vmax) / Vo)
  • Basic knowledge of sound wave propagation in biological tissues
  • Ability to convert units between mm, m, and km/s
NEXT STEPS
  • Study the principles of simple harmonic motion in biological systems
  • Learn about the Doppler Effect in various contexts, including medical applications
  • Explore sound wave propagation in different mediums, particularly biological tissues
  • Practice unit conversion techniques relevant to physics problems
USEFUL FOR

Students studying physics, particularly those focusing on medical applications of sound waves, as well as professionals in medical imaging and diagnostics who utilize Doppler technology.

rpcarroll
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Homework Statement


Suppose a heart's ventricular wall moves in simple harmonic motion with amplitude 1.8mm and a frequency of 115 per minute. (a) Given a motion detector in contact with the chest produces sound at 2,000,000Hz which travels through tissue at 1.50 km/s. Find the maximum linear speed of the heart wall. (b) Find maximum frequency at which the sound arrvies at the heart. (c) Find the maximum frequency which at which sound is received by the motion detector.

Homework Equations


f'=fo((Vo+Vmax)/Vo)

The Attempt at a Solution


(a) 115=2,000,000((1.5+Vmax)/1.5)
Vmax=1.5
I am struggling with some of the concepts and where different terms can be applied, any suggestions? Do I need to convert any units?
 
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rpcarroll said:
... simple harmonic motion with amplitude 1.8mm and ... frequency of 115 per minute.
(a) Given ... sound at 2,000,000Hz ... travels through tissue at 1.50 km/s. Find the maximum linear speed of the heart wall. (b) Find maximum frequency at which the sound arrvies at the heart. (c) Find the maximum frequency ... at which sound is received by the motion detector.
The wording of (a) is quite confusing, but I think that you don't need the info about the motion detector. (b) is ambiguous, but I would imagine you need to take into acount the doppler effect. You will have to think about (c) a bit.



rpcarroll said:
(a) 115=2,000,000((1.5+Vmax)/1.5)
Vmax=1.5
I don't think so.
 

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