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Harmonics problem

  1. Nov 29, 2006 #1
    String A is stretched between two clamps separated by distance L. String B, with the same linear density and under the same tension (i.e., having the same wave velocity) as String A, is stretched between two other clamps separated by distance 4L. Consider the first 8 harmonics of string B. For which, if any, of these 8 harmonics does the frequency matched the frequency of the following harmonics of string A:
    (a)First? 4
    (b)Second?
    (c)Third? 0


    For some reason I'm thinking that there aren't any equations to use for this sort of problem but that it is more visual. I have the first answer right because I figured that once string A is stretched to 4L it's Tension is 4T which makes it's frequencies 4xs faster than String B. However for the second harmonic I'm having a hard time figuring out, unless the frequencies slow down. Am I approaching this the right way?
     
  2. jcsd
  3. Nov 29, 2006 #2

    berkeman

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    Staff: Mentor

    I don't think A is stretched to 4T. The way I read the problem statement the two strings have the same tension, but B is 4 times as long. So which harmonic of B will have the same frequency as the fundamental of A?


    EDIT -- I had A & B backwards. Fixed it. B is 4x as long as A.
     
    Last edited: Nov 29, 2006
  4. Nov 29, 2006 #3
    << Direct answer deleted by berkeman -- please don't post the answer. Just help guide the OP to the answer with hints. >>
     
    Last edited by a moderator: Nov 29, 2006
  5. Nov 29, 2006 #4

    berkeman

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    bearhug -- just think about how the fundamental and harmonics look on a plucked string. The fundamental has a how many sine periods (or sub-periods) between the string ends? The 2nd harmonic how many full sine-periods between the ends? The 4th harmonic has how many full sine periods between the two ends? etc....
     
    Last edited: Nov 29, 2006
  6. Dec 1, 2006 #5
    Quick question, do these strings slow down at all or do I assume they are going at a constant rate. Also can the answer be a fraction?
     
  7. Dec 1, 2006 #6

    berkeman

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    Any real string will have its oscillations slow down at some damping rate, but that affects the amplitude, not the frequency. Otherwise guitars would sound pretty strange....

    The way I read the problem, they want to know which harmonics of the longer string match the fundamental of the shorter string. I could be reading it incorrectly, however.
     
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