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interference


Let us assume that the small wave has a wavelength which is given by λ1 and the larger wave a wavelength which is given by λ2.
Since the speed v is the same for the two waves as they propagate in the same medium, the periods of the two disturbances are given by

vT1 = λ1      and      vT2 = λ2


Let us, furthermore, allow for two different phases, φ1 and φ2, at t=0. Then the displacements of two individual disturbances are described by

u1(x,t) = A1 sin( 2π ( (t/T1) - (x/λ1) ) + φ1 )

     and     

u2(x,t) = A2 sin( 2π ( (t/T2) - (x/λ2) ) + φ2 )








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