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Sound of vibrating string - modes

  1. Feb 17, 2017 #1
    1. The problem statement, all variables and given/known data
    Suppose we listen to the sound of a vibrating string with a pickup that is sensitive to the motion at a point 1/3 of the string's length from one end. Which statement is true?

    A.) We will be able to hear all of the modes except the third
    B.) We will not be able to hear the third mode or the sixth mode
    C.) None of the statements above are true
    D.) We will be able to hear only the 3rd and higher modes
    E.) We will only be able to hear the 3rd mode

    2. Relevant equations
    None

    3. The attempt at a solution
    I have made a mono-cord and measured frequency at different modes for this class. We have discussed that when you excite the fundamental, you also excite all modes above it. But when you select higher modes, you won't excite the modes below it.
    So I at first tried (D) but the answer was incorrect. Then I figured that maybe by "pickup that is sensitive" it meant that the pickup could only hear the point at 1/3, so figured they would here the 3rd and 6th and so I selected (C) but that also isn't correct.
    I think I must just be misunderstanding the question all together.
     
  2. jcsd
  3. Feb 17, 2017 #2

    Delta²

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    Gold Member

    Well this is interesting, without knowing anything about modes in a string, by using logic alone and since you tell me that C is not true it means that the opposite of C is true which means that one of A or B (or both) are true. Something tells me the correct answer is A because the point located at distance 1/3 from one end of the string corresponds to a stationary point for the standing waves of 3rd mode. So this point "doesn't move " to the frequency of the 3rd mode but can move in the frequency of other modes.
     
  4. Feb 17, 2017 #3
    Thank you for your response, Delta! Your post helped me to understand the problem. The pickup is sensitive to the MOTION at a point 1/3 of the way down the string. At point 1/3, there is no movement in both the 3rd and 6th modes. So the correct answer was B. Thank you!
     
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