1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook