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Homework Help: Ultrasound reflected from an oncoming bloodstream

  1. Dec 12, 2004 #1
    Ultrasound reflected from an oncoming bloodstream that is moving at 31 cm/s is mixed with the original frequency of 1.3 MHz to produce beats. What is the beat frequency? (Velocity of sound in blood = 1540 m/s.)

    I know that there are two doppler shifts; one where the source is fixed and the other where the observer is fixed.

    So i'm supposed to use the doppler shift equation to solve for this:

    f1=f((V + Vo) / (V - Vs))

    but I dont know what numbers to plug into which variables.

    After I find the frequency of the doppler shifted echo all I have to do is subtract it from the original frequency of 1.3 MHz, right?
  2. jcsd
  3. Dec 12, 2004 #2

    Andrew Mason

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    You have used the doppler expression where the source and observer are both moving relative to the medium. You also have to keep in mind that there is a reflection so there are two doppler shifts.

    Use the moving observer form:
    [tex]f_{blood} = f_{source}(\frac{v_{sound}+ v_{blood}}{v_{sound}})[/tex]

    to find the apparent frequency that the blood receives. The blood then acts as a moving source and reflects this back to the observer so used the moving source form:

    [tex]f_{observer} = f_{blood}(\frac{v_{sound}}{v_{sound} - v_{blood}})[/tex]

    You are correct that the beat frequency is the difference between the original and the reflected sound.

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