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Interference of Waves from Two Sources and Beats

  1. Feb 6, 2010 #1
    1. The problem statement, all variables and given/known data
    Two loudspeakers emit 300 Hz notes. One speaker sits on the ground. The other speaker is in the back of a pickup truck. You hear eight beats per second as the truck drives away from you. What is the truck's speed? (Assume that the speed of sound is 343 m/s.)


    2. Relevant equations
    These equations could be useful:
    change in d= d2-d1, d1 distance is one speaker on the ground, and d2 another speaker on the truck.
    Constructive interference: change in d= m*wavelenght, m= 1,2,3,...
    Destructive interference: change in d= (m+1/2)* wavelenght, m=1,2,3,...
    f(beat)= f1-f2
    f(oscillations) = 1/2(f1+f2)

    3. The attempt at a solution
    I am not sure how to go about this problem. I tried using f(beat) formula but I am stuck. Please help.

    Thank you,
     
  2. jcsd
  3. Feb 6, 2010 #2
    The beat formula is a good start. That should tell you the frequency of the sound waves from the truck. It should be a lower frequency than the speaker on the ground, due to the motion of the truck.
    The reason it is lower is due to the Doppler Effect.
    The Doppler formula for the change in frequency due to relative motion should give you the speed of the truck.
    Do you know the formula for the Doppler Effect?
     
  4. Feb 8, 2010 #3
    formula for doppler effect is,
    change in F = +/- 2*Fo (Vo/V), F is for frequency. how can I use this equation to solve for the speed of the truck, V?
     
  5. Feb 9, 2010 #4
    I don't recognise that formula for the Doppler effect
    The observed frequency of the sound from the truck, fo, is
    fo = fv/(u+v) when the truck is moving away.
    f is original frequency the sound, v is speed of sound, u is speed of truck.
    In this formula you know
    f, fo and v
    The observed frequency we know, from the beats, is less than the original by an amount given by f - fo = fbeat
     
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