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Superposition of Harmonic Waves

  1. Feb 6, 2013 #1
    1. The problem statement, all variables and given/known data
    Find the resultant of the superpostion of two harmonic waves in the form

    E=Ecos(α-ωt)

    with amplitudes of 3 and 4 and phases of π/6 and π/2 respectively. Both waves have a period of 1s.


    2. Relevant equations

    ω=2πf = 2π/t

    3. The attempt at a solution
    I first plugged everything in so you get:

    E=3cos(π/6-2πt)
    E=4cos(π/2-2πt)

    then I used the formula

    tanα = [3sin(π/6-2πt) + 4sin(π/2-2πt)]/[3cos(π/6-2πt) + 4cos(π/2-2πt)] to get the angle. I am unsure of what to do. I understand the formula in the book conceptually for adding the two waves of different phases but I am unsure of how to use it. Thanks in advance
     
  2. jcsd
  3. Feb 6, 2013 #2

    haruspex

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    But you didn't post any such formula as a relevant equation. Or do you mean the tan α formula above? If so, what is α defined to mean in that equation?
     
  4. Feb 6, 2013 #3

    rude man

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    Expand Ecos(wt - ψ) in terms of sin and cos. Do this for both your given waves.

    Stipulate a resultant E'cos(wt - ψ'). Determine E' and ψ' by equating coefficients of the above-mentioned sines and cosines.
     
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