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The Doppler Effect and Simple Harmonic Motion question

  1. Jan 20, 2009 #1
    1. The problem statement, all variables and given/known data

    Ok heres the problem.. a little lengthy so bear with me :) (3 parts need help w/ last two)

    Expectant parents are thrilled to hear their unborn baby's heartbeat, revealed by an ultrasonic motion detector. Suppose the fetus's ventricular wall moves in simple harmonic motion with an amplitude of 1.75 mm and a frequency of 125 per minute.

    (a) Find the maximum linear speed of the heart wall. Suppose the motion detector in contact with the mother's abdomen produces sound at 2,000,000.0 Hz which travels through tissue at 1.50 km/s.

    (b) Find the difference between the original frequency and the maximum frequency at which sound arrives at the wall of the baby's heart.

    (c) Find the difference between the original frequency and the maximum frequency at which reflected sound is received by the motion detector. By electronically "listening" for echoes at a frequency different from the broadcast frequency, the motion detector can produce beeps of audible sound in synchronization with the fetal heartbeat.

    2. Relevant equations

    ω=2pi(f) where w is angular freq. and f is freq
    vmax=ωA
    f'= (v+vo/v) and f"= (v/v-vs) where vs is the speed of sound

    3. The attempt at a solution

    Ok so for part a) I determined Vmax by using Vmax=wA. No problem there. cool.

    Parts b) and c): this is where it gets really frustrating!!!

    For part b) I thought ok were doing the doppler effect. The question asks for the DIFFERENCE between FREQUENCIES. Ok, easy enough. NOT

    The answer is going to be in HZ. The sound travels through the tissue @ 1.50 km/s @ a frequency of 2000000.0 HZ and a max speed of .022925 from part a).

    I used the equation f'= f(v+vo/v)= 2000000.0Hz((1500m/s + .022925m/s)/(1500m/s).
    Right? WRONG!!!

    Plz help me... im really stumped. What am I missing here???
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 21, 2009 #2
    so you say that

    MaxVelocity = 2*PI*Frequency*Amplitude

    so that would be

    2*3.14*(125/sec)*0.00175metres

    I don't get the same figure as you do
     
  4. Jan 21, 2009 #3
    i didnt have any issues with that part.

    I was having problems with the last two parts but i figured it out. I simply forgot to subtract the answer i got from the original frequency (2000000 HZ)

    SOLVED!!!

    thnx for your input
     
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