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Angular velocity, the Doppler effect, and frequencies.

  1. Jan 29, 2010 #1
    1. The problem statement, all variables and given/known data
    A speaker is attached to a wire 1.5 m long and is spun in a circle at 2 rev/s. The speaker is connected to an electric piano on which a child is playing a note at 261 Hz. Speed of sound in air is 343 m/s.

    What range of frequencies will the stationary observer hear?

    I converted rev/s to rad/s to get angular velocity, w=720.0027707 rad/s.
    Then, I converted this into linear velocity to match with the speed of sound, v/r = w, v = 1080.004156 m/s.

    Next I used the Doppler equation for a moving source, and got 198.0887291 and 382.4685762Hz, is this correct?
     
  2. jcsd
  3. Jan 29, 2010 #2
    You can see that the linear speed of the speaker is larger than the speed of sound... no second thoughts?

    The angular velocity is 4pi rad/s (1 rev=2pi, 2rev=4pi) or approx 12.56 rad/s.
    I don't undersdtand how you can get that number (w=720.0027707 rad/s.) unless you used degrees and and a slide ruler to multiply 2 by 360.
     
  4. Jan 31, 2010 #3
    after using your 12.56 rad/s, i got 8.3733 m/s and 6.2197 to 6.5309Hz as my range of frequencies, but this does not seem right. Am I missing something?
     
  5. Feb 1, 2010 #4
    The linear velocity is given by
    v=w*r where w is the angular velocity and r is 1.5 m.
    How do you get 8.4 if w is about 12.6 and r=1.5?? It is about 19 m/s .(the 4 digits after the decimal point are pointless).

    The range of frequencies should be something around the basic frequency (261 Hz).
    Like 255-266 Hz (as an example, I did not do the calculation).
    You need to calculate the frequency increase when the source approaches the observer and the decrease when the source is going the other way.
     
  6. Feb 2, 2010 #5
    The range of velocities are 247 to 276 Hz. I divided the angular velocity by the radius instead of multiplying it (thanks for pointing that out). Also I had the variable for Vsound and V source mixed up! Thanks for the help!
     
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