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Determining interference pattern for two loudspeakers

  1. Aug 20, 2012 #1
    1. The problem statement, all variables and given/known data

    Two loudspeakers, at the same height are 2m apart and in phase with each other.Both emit 705Hz sound waves into a room. A listener stands 5m in front of the loudspeakers and 2m to one side of the centre.

    a) Is the interference pattern at this point constructive,destructive or something in between?

    b) How would the situation differ if the outputs of the loudspeakers were 180 ° out of phase?


    2. Relevant equations

    Path difference=L1-L2
    λ=v/f

    3. The attempt at a solution

    a) λ=343m/s / 705Hz = 0.486m

    Doing Pythagoras on both lengths I get L1=√5^2 +3^2 = √34m
    L2=√5^2+1^2 = √26m

    path difference=√34-√26, dividing by wavelength gives 1.504409122 so can i round that to say that m=1.5 hence there is destructive interference or do I leave the value like that and say it is something in between?

    b) phase difference=∏=mλ=path difference = m=∏-0.7319/ 0.486 = 4.958

    Again can I round up to say that m=5 so there is constructive interference since there the number of wavelengths is a whole integer.

    A bit confused on the values im getting and whether I can round, could someone check my answers?
     
  2. jcsd
  3. Aug 20, 2012 #2

    berkeman

    User Avatar

    Staff: Mentor

    I think you have it right. The differences are less than a percent from full destructive and constructive interference, so I'd go with those answers myself.
     
  4. Aug 21, 2012 #3
    Ok, thanks :)
     
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