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Homework Help: Physics-Wave concepts/standing waves

  1. Jul 12, 2010 #1
    1. The problem statement, all variables and given/known data
    A string is tied on both ends and under a tension FT. A standing wave is formed on the string. For each of the following statements select the correct option.
    1.)If the distance between the two fixed ends of the string is increased, the wavelength that corresponds to the fundamental frequency ....
    2.) When the amplitude of the wave is decreased, the fundamental frequency ....
    3.) If the distance between the two fixed ends of the string is decreased, the fundamental frequency....
    4.) If the distance between the two fixed ends of the string is increased, the wave speed ....
    5.) When the tension of the string is increased, the fundamental frequency....
    **for each number, the answer (which is the end to the sentence) is either increases, decreases, or stays the same.**

    2. Relevant equations

    I'm not really sure what relevant equations would be. I know f=v/wavelength....

    3. The attempt at a solution

    I've tried a solution with many different combinations of the answer, but I am still unable to figure it out....even after thoroughly reviewing the material in the book/notes.
     
  2. jcsd
  3. Jul 12, 2010 #2

    kuruman

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    You need additional relevant equations. Reread the book and see if you can spot them.

    1. What equation gives the fundamental frequency for a standing wave on a string?
    2. What equation relates the tension and the wave speed?
     
  4. Jul 12, 2010 #3
    v=sqrt(tension force/mu) where mu is mass/length. the fundamental frequency would be the wave speed/wavelength....
     
  5. Jul 12, 2010 #4

    kuruman

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    And how is the wavelength of the fundamental related to the distance between the fixed ends?
     
  6. Jul 12, 2010 #5
    wavelength=wave speed/fundamental frequency
     
  7. Jul 12, 2010 #6

    kuruman

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    Not what I asked. How is the distance in meters between the two fixed ends of the string related to the wavelength in meters. In other words, if the distance between the two fixed ends is L, how is L related to λ?
     
  8. Jul 12, 2010 #7
    oh ok, Sorry!

    Does L equal the wavelength?
     
  9. Jul 12, 2010 #8

    kuruman

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    No. Look at the figure in your textbook showing the fundamental standing wave pattern. The fundamental (first harmonic) has zero nodes, the second harmonic has one. Which one represents a full wavelength?
     
  10. Jul 12, 2010 #9
    okay, I think I see. The second harmonic is one full wavelength, and the first (fundamental) is half of a wavelength.
     
  11. Jul 12, 2010 #10
    would that mean 1,2,3,5 would have the answer stay the same? I'm still not sure....
     
  12. Jul 12, 2010 #11

    kuruman

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    Correct. So you can say that for the fundamental λ = 2L. Now can you answer question 1? If yes, then can you write an expression relating f, v and L?
     
  13. Jul 12, 2010 #12
    Would one be stays the same because the fundamental frequency is constant?
    Is v/f=2L the expression?
     
  14. Jul 12, 2010 #13

    kuruman

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    Not quite. The question is

    "If the distance between the two fixed ends of the string is increased, the wavelength that corresponds to the fundamental frequency _________"

    You know that

    "the distance between the two fixed ends of the string" = L
    and that for the fundamental frequency
    λ = 2L
    so what's the answer and why?
    Yes, but I would rewrite this as

    [tex]f=\frac{v}{2L}[/tex]

    Now question 3 asks "If the distance between the two fixed ends of the string is decreased, the fundamental frequency _____" What do you think? What happens to f if L is decreased?
     
  15. Jul 12, 2010 #14
    Would it increase because the L is bigger?

    Then for #3, it would decrease?
     
  16. Jul 12, 2010 #15

    kuruman

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    Correct on both accounts. Now before we proceed, let's take stock of what equations we have.

    [tex]v=\lambda f_1 \ \ (1)[/tex]

    [tex]f_1=\frac{v}{2L} \ \ (2)[/tex]

    [tex]v=\sqrt{Tension/\mu} \ \ (3)[/tex]

    Now how do you think you should answer questions 2 and 4?
     
    Last edited: Jul 12, 2010
  17. Jul 12, 2010 #16
    I honestly am not sure about #2. Do the amplitude and the fundamental frequency have any relation?

    For #4, would I look at equation 2 and make it v=f*2L?

    PS: Thank-you for your help and patience. I am slowly understanding. :)
     
  18. Jul 12, 2010 #17

    kuruman

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    There is no amplitude anywhere in the three equations, and that's all there is. So if A is not related to any of the quantities including f, what happens to A if L is decreased?

    That relation is certainly true. Now you know that L is increased? What about v? Does it increase, decrease or stay the same? Hint: What does equation (3) say about that?

    You are welcome. I am trying to teach you what I call "equation interpretation." Equations do much more than giving you a number when you put in other numbers. They express relationships between quantities.
     
  19. Jul 12, 2010 #18
    Since A is not related to any equations involving f, decreasing it would not make a difference to the fundamental frequency, so the f would stay the same, even if L is increased?

    and v would decrease with an increase in the length?
     
  20. Jul 12, 2010 #19

    kuruman

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    That is correct.

    Why do you say that? Which one of the three equations are you invoking? Look at them carefully and think what changes when L changes.
     
  21. Jul 12, 2010 #20
    Would the speed stay the same because the frequency is what depends on the length?
     
  22. Jul 12, 2010 #21

    kuruman

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    Yes, the speed will stay the same because equation (3) says that "as long as the tension and μ stay the same, v stays the same." Do you see how it works?

    To answer the last question, put equation (3) in equation (2) and interpret what you get in terms of what is being asked. I have to sign off right now, but I will check back in a couple of hours or so.
     
  23. Jul 12, 2010 #22
    When I combine equations 2 and 3, it looks to me like an increase in the tension will cause an increase in the fundamental frequency....

    ok, sounds good! I will check back later too. Thank-you again!
     
  24. Jul 12, 2010 #23

    kuruman

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    That is correct. Think of the application, when you tighten a guitar string the tone (frequency) goes up, does it not?
     
  25. Jul 12, 2010 #24
    ok great!

    So, 1.) increase 2.)stays the same 3.)decrease 4.)stays the same 5.)increase

    Is this correct? Thanks again for helping!!
     
  26. Jul 12, 2010 #25
    I think I am missing something because I put that in my answer, and it said it was wrong.... :(
     
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