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A question about wave motion and beat frequency

  1. Jan 8, 2017 #1
    1. The problem statement, all variables and given/known data
    3 tuning forks of frequencies 200, 203, 207 Hz are sounded together.find out the beat frequency.

    2. Relevant equations
    Beat frequency= n1-n2 (n=frequency).

    3. The attempt at a solution
    I know that beat frequency is the difference in the frequencies of two superposing notes. But here 3 wave frequencies are given the difference between the first 2 is 3 while between 203, 207 is 4 .How to find the beat frequency of all 3 waves together? I have even tried finding beat frequency of the lowest and highest frequency and got 7 but still it's not the answer.how to solve these kinds sum any little help will be greatly helpful :)
     
  2. jcsd
  3. Jan 8, 2017 #2

    haruspex

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    You need to start with a general concept of what a beat frequency is. How would you define it?
     
  4. Jan 8, 2017 #3
    Beats per second.i.e. difference between 2 interfering waves' frequency
     
  5. Jan 8, 2017 #4

    haruspex

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    No, that doesn't define beat frequency.
    Try defining it in terms of what you hear, or in terms of what you would see if you graphed the amplitude over time.
     
  6. Jan 9, 2017 #5
    Let me say that it's the interference of the two waves with different frequency but same amplitude?!
     
  7. Jan 9, 2017 #6

    haruspex

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    No, you still miss the point of the question. Why are we interested in beat frequencies at all? Why do we call them beat frequencies? What do you hear when they occur? What do you notice if you look at a graph of interference between nearby frequencies?
     
  8. Jan 10, 2017 #7
    Sorry I just couldn't figure out about what you are talking. And still I'm confused about that question :/ how to find the beat frequency of three superposed waves? Just today I found another question like that which says n+1, n, n-1 are the frequencies of three superimposed waves.now what will be their beat frequency? I guess I'm missing something cause I thought 1 to be it's answer which is contrast to the original answer I.e. 2 . Can you help me on how to find beat frequency when more than 2 waves say as here it's 3 is superimposed? This question is really depressing :(
     
  9. Jan 10, 2017 #8

    haruspex

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    If you do not know what "beat frequency" means, what hope do you have of calculating it?

    The question I am asking is not that difficult. Look at this picture of two superimposed frequencies producing a beat:
    https://en.wikipedia.org/wiki/File:Beating_Frequency.svg
    In terms of the picture, what is the period of one beat?
     
    Last edited: Jan 10, 2017
  10. Jan 21, 2017 #9

    haruspex

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    It "beats" me why you find this so hard to answer, but I'll explain: When a beat is produced by a combination of sound waves, it means that to the listener it seems like there is a rhythmic change in amplitude. Looking at the diagram, the beats are the highest peaks in amplitude.

    The highest peaks occur, of course, when the individual waves come most closely into phase. With two pure sine waves, one with period 2 and one with period 3 (whatever time units), if they are perfectly in phase at time 0, when will they next be perfectly in phase?
     
  11. Jan 23, 2017 #10
    sorry for taking much time to reply. *assisgments -_- * coming back to the question they will be in phase after completing one cycle which will be equal to it's time period T o_O
     
  12. Jan 23, 2017 #11

    haruspex

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    Yes, but I gave you specific numbers for the individual periods: 2 and 3. So what is the beat period, as a number?
     
  13. Jan 23, 2017 #12
    one? they will meet after one period?
     
  14. Jan 23, 2017 #13

    haruspex

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    Draw a diagram. One peaks every 2 seconds (say) and the other every 3.
     
  15. Jan 23, 2017 #14
    after T=2.5 sec?
     
  16. Jan 23, 2017 #15

    haruspex

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    Are you just guessing or did you draw a diagram? If you drew one, please try to post it.
     
  17. Jan 24, 2017 #16
    1485273657972.jpg
     
  18. Jan 24, 2017 #17
    I have included a rough graph.sorry for it's incoherence.i know it's too poorly picturised :/ but @haruspex (sorry if I spelt your name incorrectly) beg you please explain me how to do it at least now :(
     
  19. Jan 24, 2017 #18
    And in that graph that I have drawn, it's clear that first they meet at 2.5 seconds and then at 4.5 I.e. again after 2.5 seconds.correct me if I am wrong? But how could I relate this to get the answer to the question that I've posted!
     
  20. Jan 24, 2017 #19

    haruspex

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    You appear to have drawn one of period 4 and one of period 5. They started 180 out of phase (one is going up and the other down).
    At the 4.5 mark, they are not both back where they started. At a point where they have both completed a whole number of cycles, each should continue exactly as it did from time 0, i.e. both at the x axis, with the red line going down and the other up.

    Mark 12 equal intervals on the x axis. Have both curves rising from the origin. The period 2 curve goes down through the x axis at t=2, 6 and 10, and up through it at 0, 4 and 8. The period 3 goes down through the x axis at 3 and 9, and up through it at 0, 6 and 12.
     
  21. Jan 24, 2017 #20

    haruspex

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    upload_2017-1-25_9-21-59.png
    Here are three sine waves of the same amplitude, all starting in phase. Can you figure out what the three periods are?
    Can you find the time at which a pair of them are both back to their starting state? (There are two such pairs.)
    Can you see how the time for two to get back into phase relates to their individual periods?
    When will all three be back in phase?
     

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