Determing frequency shift of an ultrasound

  1. 1. The problem statement, all variables and given/known data
    A Doppler blood flow unit emits ultrasound at 5.0 MHz.

    What is the frequency shift of the ultrasound reflected from blood moving in an artery at a speed of 0.20 m/s?

    Express your answer using two significant figures.

    2. Relevant equations
    f' = f0(v/v-Vs)
    frequency shift = f' - f0

    f0 = 5*10^6 Hz
    v = 1500 m/s (assumed)
    Vs = 0.20 m/s


    3. The attempt at a solution
    Plugging in the numbers we get the following equation for frequency shift:

    (5*10^6)*[1500/(1500-0.2)]-5*10^6

    Which comes out to approx 666 Hz. or 6.7 *10^2 Hz using 2 significant figures. However, this problem comes from an online hw set and according to that 6.7 *10^2 is not the correct solution.

    Does anyone have an idea of what I am doing wrong? Thanks in advance for any and all help!
     
    Last edited: Mar 19, 2010
  2. jcsd
  3. rl.bhat

    rl.bhat 4,435
    Homework Helper

    Hi grigri9, welcome to PF.
    We have here a case of the "listener" (the blood corpuscles) moving away from a stationary source, and thus the frequency, f corpuscle that will be reflected by the corpuscles will be
    f corpuscle = f(transmitted)[(Vs - Vb)/Vs

    For the reflected waves, reflection, the corpuscles are the source and the "listener" is the receiver. The frequency at the receiver will be
    f(receiver) = f(corpuscles)*Vs/(Vs + Vb)

    from which we get
    f(receiver) = f(transmitted)*(Vs-Vb)/(Vs+Vb)
     
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