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Two in-phase loudspeakers on a coordinate plane

  1. Sep 15, 2009 #1
    1. The problem statement, all variables and given/known data
    Two in-phase loudspeakers are located at (x, y) coordinates (-3.0, +2.0) and (-3.0, -2.0) . They emit identical sound waves with a 2.0 m wavelength and amplitude a.

    Determine the amplitude of the sound at the five positions on the y-axis (x=0):
    with y=0.0
    with y=0.5
    with y=1.0
    with y=1.5
    with y=2.0

    2. Relevant equations
    k=2pi/wavelength
    D(x,t)=A(x)cos(wt)
    phase change = [2pi(path-length difference)]/(wavelength) + (initial phase change)

    Don't know what other equations I need

    3. The attempt at a solution
    I could find the phase change, but I can't see how that will relate to the amplitude because I don't have the angular frequency or displacement.

    Variables I can find: path-length difference, wavelength, k, phase change
     
  2. jcsd
  3. Sep 15, 2009 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi tiger1! Welcome to PF! :smile:

    (have a pi: π and an omega: ω :wink:)
    You do have the angular frequency … it's ω.

    using the usual trignometric identities, you can show that the sum of Acos(ωt + θ) to Acos(ωt + φ) is of the form Bcos(ωt + ψ). :wink:
     
  4. Sep 15, 2009 #3
    Figured it out using A=|2a cos[1/2(change in phi)]|
     
    Last edited: Sep 15, 2009
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