Transverse Wave Interference

  1. 1. The problem statement, all variables and given/known data

    What phase difference between two otherwise identical traveling waves, moving in the same direction along a stretched string, will result in the combined wave having an amplitude 1.3 times that of the common amplitude of the two combining waves? Express your answer in (a) degrees, (b) radians, and (c) as a fraction of the wavelength.

    2. Relevant equations

    Same frequency and amplitudes results in:

    y(x,t)=2ymcos(1/2Φ)sin(kx +/- wt +.5Φ)


    3. The attempt at a solution

    Amplitude of resultant wave = 2ymcos(1/2Φ)

    2ymcos(1/2Φ)=2.3ym

    solving for Φ :

    2arccos(1.3/2)=Φ which is 1.7rad

    However, I'm not sure how to express this in terms of the wavelength.
     
  2. jcsd
  3. lewando

    lewando 1,077
    Gold Member

    Just looking for fraction of the wavelength. A whole wavelength would be 2*pi rad worth of phase, yes?
     
  4. That's what I had thought. Actually, I had done: 1.7/2pi, but I didn't put parenthesis around 2pi on my calculator. Jeez. Well, I guess the semester just started. Thank you lewando!
     
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