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Homework Help: PLEASE HELP Speakers and Sound- simple problem!

  1. Apr 15, 2010 #1
    PLEASE HELP!!! Speakers and Sound--- simple problem!

    Two radio speakers produce sound with a wavelength of 0.800 m. If the two speakers are separated by 1.00 m as shown in the diagram, how close to speaker A can a person stand and not hear the sound they produce?

    DIAGRAM:

    [A] --------d---------- person
    |
    |
    |


    where [A] and are the speakers (they are 1.00 m apart)

    The answer is d=1.05m

    How do i solve this problem?

    i know that in order not to hear sound, it must be destructive interference, so when the wavelengths reach the person, they must be out of phase = [m + 0.5(lambda)] where m=0,1,2...

    I dont know what kind of formula to use... please help! :(
     
  2. jcsd
  3. Apr 15, 2010 #2

    kuruman

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    Re: PLEASE HELP!!! Speakers and Sound--- simple problem!

    For destructive interference, the path length difference from the sources to the person must be λ/2, or 3λ/2 or 5λ/2 or any odd number multiplied by λ/2. Here you want the closest distance the person can be, so the path length difference must be λ/2. Can you find the path length difference?
     
  4. Apr 15, 2010 #3
    Re: PLEASE HELP!!! Speakers and Sound--- simple problem!

    Path length difference = λ/2 = 0.8/2 = 0.4 m

    But now what would I do?
     
  5. Apr 15, 2010 #4
    Re: PLEASE HELP!!! Speakers and Sound--- simple problem!

    I'm not sure if this is the 'correct' method... but if i use a2 + b2 = c2

    then 12 + x2 = (x+0.4)2
    1 - 0.8x -0.16 = 0
    x= 0.84/0.8 = 1.05 m
     
  6. Apr 16, 2010 #5

    kuruman

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    Re: PLEASE HELP!!! Speakers and Sound--- simple problem!

    If L1 is the distance from the person to the closest speaker and L2 is the distance to the farthest speaker, then the path length difference is L2 - L1. Can you find expressions for L1 and L2 in terms of the given quantities and according to the drawing you have posted?
     
  7. Apr 16, 2010 #6
    Re: PLEASE HELP!!! Speakers and Sound--- simple problem!

    hmmm... I've been trying but i can't think of something that works.. :(
     
  8. Apr 16, 2010 #7

    kuruman

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    Re: PLEASE HELP!!! Speakers and Sound--- simple problem!

    In your drawing you have a triangle marked by the vertices "a", "b" and "person". Which side should be labeled L1 and which side should be labeled L2?
     
  9. Apr 16, 2010 #8
    Re: PLEASE HELP!!! Speakers and Sound--- simple problem!

    L2 should be the distance between speaker b and the person.
    L1 should be the distance between speak a and the person.
    right? now what?
     
  10. Apr 16, 2010 #9

    kuruman

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    Re: PLEASE HELP!!! Speakers and Sound--- simple problem!

    Back to my earlier posting.

     
  11. Apr 16, 2010 #10
    Re: PLEASE HELP!!! Speakers and Sound--- simple problem!

    the only thing i can think of is using Pythagorean theorem for this question..

    is there a specific formula or expression relating sound waves and path length difference? i don't know one...
     
  12. Apr 16, 2010 #11

    kuruman

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    Re: PLEASE HELP!!! Speakers and Sound--- simple problem!

    Use the Pythagorean theorem and find the difference between the two lengths. That difference should be set equal to half a wavelength. Solve the equation to find d.
     
  13. Apr 16, 2010 #12
    Re: PLEASE HELP!!! Speakers and Sound--- simple problem!

    thats exactly what i did? haha
    thanks :P
     
  14. Apr 16, 2010 #13

    kuruman

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    Re: PLEASE HELP!!! Speakers and Sound--- simple problem!

    So what's the answer?
     
  15. Apr 18, 2010 #14
    Re: PLEASE HELP!!! Speakers and Sound--- simple problem!

    d= 1.05 m
     
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