Anonymous
Anonymous asked in Science & MathematicsPhysics · 3 weeks ago

Comparing the waves y1=A*e^(i(k+b)x) y2=B*e^(i(kx+a)), the difference in wavelength for the two waves will depend on b right?

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  • mars
    Lv 7
    3 weeks ago

    Yes............

  • 3 weeks ago

    The real coefficient1in front of the 'x' equals 2π/λ.

    For example if we have e^(24ix) then

    24 = 2π/λ

    λ =  2π/24 =  π/12

    In e^(i(k+b)x) this coefficient is (k+b) giving:

    k+b = 2π/λ

    λ =  2π/(k+b)

    In e^(i(kx+a)) this coefficient is k giving:

    k = 2π/λ

    λ = 2π/k

    So the difference in wavelengths is:

    Δλ = 2π/k – 2π/(k+b)

    = 2π(1/k – 1/(k+b))

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