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Homework Help: Finding unknown frequency from beats?

  1. Dec 15, 2009 #1
    Finding unknown frequency from beats???

    1. The problem statement, all variables and given/known data

    i have to find the unknown resonant frequency of a tuning fork??

    2. Relevant equations

    when this unknown is struck along a known freq of 360 hertz = you hear beat frequency of 2 hertz.. and when its struck alongside a known freq of 358 = you hear beat frequncy of 4 hertz what is the frequency of the unknown tuning fork?????

    3. The attempt at a solution

    i have no clue please help me
     
  2. jcsd
  3. Dec 15, 2009 #2

    Ouabache

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    Re: Finding unknown frequency from beats???

    what is the relationship between any two fork frequencies sounded together and the beat frequency generated? (hint: look in your text and your lab documents)
     
  4. Dec 15, 2009 #3
    Re: Finding unknown frequency from beats???

    Ouabache= the relation is when two similar frequencies are heard= a beat is generated

    and freq of beat= freq1 -freq 2 therefore... my textbook doesnt have any sample questions thats y please help me with more direct answer.. or atleast one or two steps

    one attempt i made was let unknown freq be x
    thus x + 360 hz = beat freq of 2 hz
    x+ 358 hz = beat freq of 4 hz

    but i dont know if i can solve x unknown frequency now
     
  5. Dec 15, 2009 #4
    Re: Finding unknown frequency from beats???

    The beat frequency depends on the difference, not the sum; as you correctly said initially.
    You know the difference is 2 but you don't know which one is the higher.
    So, the clue to that is to look at the one where the difference was 4.
     
  6. Dec 15, 2009 #5
    Re: Finding unknown frequency from beats???

    if the difference is 4 hertz that means

    the unknown frequency will be 362 hertz

    because the formula is freq of beat = f2 - f1
    thus difference of 4 hertz means 362- 358

    is this correct please give me more hints im stuck here
     
  7. Dec 15, 2009 #6
    Re: Finding unknown frequency from beats???

    That's correct.
    It is 2 more than 360 and 4 more than 358.
    so 2=362-360 (beat frequ of 2)
    and
    4=362-358 (beat frequ of 4)
    362 is the only frequency that satisfies both equations.
     
  8. Dec 15, 2009 #7

    Ouabache

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    Re: Finding unknown frequency from beats???

    An intuitive way to solve this...
    When you strike a known fork against the unknown and you don't hear any beats at all, then their difference in frequency is zero |f2-f1|=0 or f1 = f2

    When you were given the 2nd bit of information, where the known fork = 358Hz, the beat frequency "increased" to 4Hz, but you want the beats to decrease to zero..
    So you know immediately, that the unknown frequency must be > 360Hz ..
    For |360-f1| = 2Hz, f1 = 362Hz.
     
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